KILLED
proof of input_6H7Cbmgixr.trs
# AProVE Commit ID: aff8ecad908e01718a4c36e68d2e55d5e0f16e15 fuhs 20220216 unpublished


The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF).

(0) CpxTRS
(1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
(2) CpxTRS
(3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
(4) CpxTRS
(5) RelTrsToWeightedTrsProof [UPPER BOUND(ID), 0 ms]
(6) CpxWeightedTrs
    (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (8) CpxTypedWeightedTrs
    (9) CompletionProof [UPPER BOUND(ID), 0 ms]
    (10) CpxTypedWeightedCompleteTrs
        (11) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (12) CpxTypedWeightedCompleteTrs
        (13) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 13 ms]
        (14) CpxRNTS
        (15) SimplificationProof [BOTH BOUNDS(ID, ID), 7 ms]
        (16) CpxRNTS
        (17) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms]
        (18) CpxRNTS
        (19) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
        (20) CpxRNTS
        (21) IntTrsBoundProof [UPPER BOUND(ID), 200 ms]
        (22) CpxRNTS
        (23) IntTrsBoundProof [UPPER BOUND(ID), 70 ms]
        (24) CpxRNTS
        (25) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
        (26) CpxRNTS
        (27) IntTrsBoundProof [UPPER BOUND(ID), 255 ms]
        (28) CpxRNTS
        (29) IntTrsBoundProof [UPPER BOUND(ID), 57 ms]
        (30) CpxRNTS
        (31) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
        (32) CpxRNTS
        (33) IntTrsBoundProof [UPPER BOUND(ID), 183 ms]
        (34) CpxRNTS
        (35) IntTrsBoundProof [UPPER BOUND(ID), 86 ms]
        (36) CpxRNTS
        (37) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
        (38) CpxRNTS
        (39) IntTrsBoundProof [UPPER BOUND(ID), 180 ms]
        (40) CpxRNTS
        (41) IntTrsBoundProof [UPPER BOUND(ID), 5 ms]
        (42) CpxRNTS
        (43) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
        (44) CpxRNTS
        (45) IntTrsBoundProof [UPPER BOUND(ID), 23.8 s]
        (46) CpxRNTS
        (47) IntTrsBoundProof [UPPER BOUND(ID), 7636 ms]
        (48) CpxRNTS
    (49) CompletionProof [UPPER BOUND(ID), 0 ms]
    (50) CpxTypedWeightedCompleteTrs
        (51) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
        (52) CpxRNTS
(53) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms]
(54) CdtProblem
    (55) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
    (56) CdtProblem
    (57) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (58) CdtProblem
    (59) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 11 ms]
    (60) CdtProblem
    (61) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (62) CdtProblem
    (63) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (64) CdtProblem
    (65) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (66) CdtProblem
    (67) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (68) CdtProblem
    (69) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 1 ms]
    (70) CdtProblem
    (71) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 84 ms]
    (72) CdtProblem
    (73) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (74) CdtProblem
    (75) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (76) CdtProblem
    (77) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (78) CdtProblem
    (79) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (80) CdtProblem
    (81) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (82) CdtProblem
    (83) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (84) CdtProblem
    (85) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 12 ms]
    (86) CdtProblem
    (87) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (88) CdtProblem
    (89) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 5 ms]
    (90) CdtProblem
    (91) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (92) CdtProblem
    (93) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 3 ms]
    (94) CdtProblem
    (95) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 15 ms]
    (96) CdtProblem
    (97) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (98) CdtProblem
    (99) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 4 ms]
    (100) CdtProblem
    (101) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 6 ms]
    (102) CdtProblem
    (103) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 386 ms]
    (104) CdtProblem
    (105) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (106) CdtProblem
    (107) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (108) CdtProblem
    (109) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 338 ms]
    (110) CdtProblem
    (111) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (112) CdtProblem
    (113) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (114) CdtProblem
    (115) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (116) CdtProblem
    (117) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (118) CdtProblem
    (119) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (120) CdtProblem
    (121) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (122) CdtProblem
    (123) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 14 ms]
    (124) CdtProblem
    (125) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (126) CdtProblem
    (127) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (128) CdtProblem
    (129) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms]
    (130) CdtProblem
    (131) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (132) CdtProblem
    (133) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (134) CdtProblem
    (135) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (136) CdtProblem
    (137) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (138) CdtProblem
    (139) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (140) CdtProblem
    (141) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (142) CdtProblem
    (143) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 4 ms]
    (144) CdtProblem
    (145) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (146) CdtProblem
    (147) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms]
    (148) CdtProblem
    (149) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (150) CdtProblem
    (151) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (152) CdtProblem
    (153) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (154) CdtProblem
    (155) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (156) CdtProblem
    (157) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (158) CdtProblem
    (159) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (160) CdtProblem
    (161) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (162) CdtProblem
    (163) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms]
    (164) CdtProblem
    (165) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (166) CdtProblem
    (167) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (168) CdtProblem
    (169) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms]
    (170) CdtProblem
    (171) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (172) CdtProblem
    (173) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (174) CdtProblem
    (175) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms]
    (176) CdtProblem
    (177) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (178) CdtProblem
    (179) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (180) CdtProblem
    (181) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms]
    (182) CdtProblem
    (183) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (184) CdtProblem
    (185) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (186) CdtProblem
    (187) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2 ms]
    (188) CdtProblem
    (189) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (190) CdtProblem
    (191) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 22 ms]
    (192) CdtProblem
    (193) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (194) CdtProblem
    (195) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (196) CdtProblem
    (197) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms]
    (198) CdtProblem
    (199) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (200) CdtProblem
    (201) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (202) CdtProblem
    (203) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (204) CdtProblem
    (205) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms]
    (206) CdtProblem
    (207) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 7 ms]
    (208) CdtProblem
    (209) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 3 ms]
    (210) CdtProblem
    (211) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 28 ms]
    (212) CdtProblem
    (213) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (214) CdtProblem
    (215) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 16 ms]
    (216) CdtProblem
    (217) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (218) CdtProblem
    (219) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (220) CdtProblem
    (221) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (222) CdtProblem
    (223) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms]
    (224) CdtProblem
    (225) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 7 ms]
    (226) CdtProblem
    (227) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (228) CdtProblem
    (229) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (230) CdtProblem
    (231) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms]
    (232) CdtProblem
    (233) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (234) CdtProblem
    (235) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (236) CdtProblem
    (237) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 22 ms]
    (238) CdtProblem
    (239) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 14 ms]
    (240) CdtProblem
    (241) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms]
    (242) CdtProblem
    (243) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (244) CdtProblem
    (245) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (246) CdtProblem
    (247) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms]
    (248) CdtProblem
    (249) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (250) CdtProblem
    (251) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1 ms]
    (252) CdtProblem
    (253) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (254) CdtProblem
    (255) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (256) CdtProblem
    (257) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (258) CdtProblem
    (259) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 16 ms]
    (260) CdtProblem
    (261) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms]
    (262) CdtProblem
    (263) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (264) CdtProblem
    (265) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (266) CdtProblem
    (267) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 7 ms]
    (268) CdtProblem
    (269) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (270) CdtProblem
    (271) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (272) CdtProblem
    (273) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 7 ms]
    (274) CdtProblem
    (275) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (276) CdtProblem
    (277) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (278) CdtProblem
    (279) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms]
    (280) CdtProblem


----------------------------------------

(0)
Obligation:
The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF).


The TRS R consists of the following rules:

   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(x)))) -> check(s(x))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(x))) -> s(half(x))
   plus(0, y) -> y
   plus(s(x), y) -> s(plus(x, y))
   times(x, y) -> timesIter(x, y, 0)
   timesIter(x, y, z) -> if(check(x), x, y, z, plus(z, y))
   p(s(x)) -> x
   p(0) -> 0
   if(zero, x, y, z, u) -> z
   if(odd, x, y, z, u) -> timesIter(p(x), y, u)
   if(even, x, y, z, u) -> plus(timesIter(half(x), y, half(z)), timesIter(half(x), y, half(s(z))))

S is empty.
Rewrite Strategy: PARALLEL_INNERMOST
----------------------------------------

(1) RenamingProof (BOTH BOUNDS(ID, ID))
Renamed function symbols to avoid clashes with predefined symbol.
----------------------------------------

(2)
Obligation:
The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF).


The TRS R consists of the following rules:

   check(0') -> zero
   check(s(0')) -> odd
   check(s(s(0'))) -> even
   check(s(s(s(x)))) -> check(s(x))
   half(0') -> 0'
   half(s(0')) -> 0'
   half(s(s(x))) -> s(half(x))
   plus(0', y) -> y
   plus(s(x), y) -> s(plus(x, y))
   times(x, y) -> timesIter(x, y, 0')
   timesIter(x, y, z) -> if(check(x), x, y, z, plus(z, y))
   p(s(x)) -> x
   p(0') -> 0'
   if(zero, x, y, z, u) -> z
   if(odd, x, y, z, u) -> timesIter(p(x), y, u)
   if(even, x, y, z, u) -> plus(timesIter(half(x), y, half(z)), timesIter(half(x), y, half(s(z))))

S is empty.
Rewrite Strategy: PARALLEL_INNERMOST
----------------------------------------

(3) RelTrsToTrsProof (UPPER BOUND(ID))
transformed relative TRS to TRS
----------------------------------------

(4)
Obligation:
The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF).


The TRS R consists of the following rules:

   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(x)))) -> check(s(x))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(x))) -> s(half(x))
   plus(0, y) -> y
   plus(s(x), y) -> s(plus(x, y))
   times(x, y) -> timesIter(x, y, 0)
   timesIter(x, y, z) -> if(check(x), x, y, z, plus(z, y))
   p(s(x)) -> x
   p(0) -> 0
   if(zero, x, y, z, u) -> z
   if(odd, x, y, z, u) -> timesIter(p(x), y, u)
   if(even, x, y, z, u) -> plus(timesIter(half(x), y, half(z)), timesIter(half(x), y, half(s(z))))

S is empty.
Rewrite Strategy: PARALLEL_INNERMOST
----------------------------------------

(5) RelTrsToWeightedTrsProof (UPPER BOUND(ID))
Transformed relative TRS to weighted TRS
----------------------------------------

(6)
Obligation:
The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, INF).


The TRS R consists of the following rules:

   check(0) -> zero [1]
   check(s(0)) -> odd [1]
   check(s(s(0))) -> even [1]
   check(s(s(s(x)))) -> check(s(x)) [1]
   half(0) -> 0 [1]
   half(s(0)) -> 0 [1]
   half(s(s(x))) -> s(half(x)) [1]
   plus(0, y) -> y [1]
   plus(s(x), y) -> s(plus(x, y)) [1]
   times(x, y) -> timesIter(x, y, 0) [1]
   timesIter(x, y, z) -> if(check(x), x, y, z, plus(z, y)) [1]
   p(s(x)) -> x [1]
   p(0) -> 0 [1]
   if(zero, x, y, z, u) -> z [1]
   if(odd, x, y, z, u) -> timesIter(p(x), y, u) [1]
   if(even, x, y, z, u) -> plus(timesIter(half(x), y, half(z)), timesIter(half(x), y, half(s(z)))) [1]

Rewrite Strategy: INNERMOST
----------------------------------------

(7) TypeInferenceProof (BOTH BOUNDS(ID, ID))
Infered types.
----------------------------------------

(8)
Obligation:
Runtime Complexity Weighted TRS with Types.
The TRS R consists of the following rules:

   check(0) -> zero [1]
   check(s(0)) -> odd [1]
   check(s(s(0))) -> even [1]
   check(s(s(s(x)))) -> check(s(x)) [1]
   half(0) -> 0 [1]
   half(s(0)) -> 0 [1]
   half(s(s(x))) -> s(half(x)) [1]
   plus(0, y) -> y [1]
   plus(s(x), y) -> s(plus(x, y)) [1]
   times(x, y) -> timesIter(x, y, 0) [1]
   timesIter(x, y, z) -> if(check(x), x, y, z, plus(z, y)) [1]
   p(s(x)) -> x [1]
   p(0) -> 0 [1]
   if(zero, x, y, z, u) -> z [1]
   if(odd, x, y, z, u) -> timesIter(p(x), y, u) [1]
   if(even, x, y, z, u) -> plus(timesIter(half(x), y, half(z)), timesIter(half(x), y, half(s(z)))) [1]

The TRS has the following type information:
check :: 0:s -> zero:odd:even
0 :: 0:s
zero :: zero:odd:even
s :: 0:s -> 0:s
odd :: zero:odd:even
even :: zero:odd:even
half :: 0:s -> 0:s
plus :: 0:s -> 0:s -> 0:s
times :: 0:s -> 0:s -> 0:s
timesIter :: 0:s -> 0:s -> 0:s -> 0:s
if :: zero:odd:even -> 0:s -> 0:s -> 0:s -> 0:s -> 0:s
p :: 0:s -> 0:s

Rewrite Strategy: INNERMOST
----------------------------------------

(9) CompletionProof (UPPER BOUND(ID))
The transformation into a RNTS is sound, since:

(a) The obligation is a constructor system where every type has a constant constructor,

(b) The following defined symbols do not have to be completely defined, as they can never occur inside other defined symbols:

   times_2

(c) The following functions are completely defined:

   check_1
   plus_2
   timesIter_3
   half_1
   p_1
   if_5

Due to the following rules being added:
none

And the following fresh constants: none

----------------------------------------

(10)
Obligation:
Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is:

Runtime Complexity Weighted TRS with Types.
The TRS R consists of the following rules:

   check(0) -> zero [1]
   check(s(0)) -> odd [1]
   check(s(s(0))) -> even [1]
   check(s(s(s(x)))) -> check(s(x)) [1]
   half(0) -> 0 [1]
   half(s(0)) -> 0 [1]
   half(s(s(x))) -> s(half(x)) [1]
   plus(0, y) -> y [1]
   plus(s(x), y) -> s(plus(x, y)) [1]
   times(x, y) -> timesIter(x, y, 0) [1]
   timesIter(x, y, z) -> if(check(x), x, y, z, plus(z, y)) [1]
   p(s(x)) -> x [1]
   p(0) -> 0 [1]
   if(zero, x, y, z, u) -> z [1]
   if(odd, x, y, z, u) -> timesIter(p(x), y, u) [1]
   if(even, x, y, z, u) -> plus(timesIter(half(x), y, half(z)), timesIter(half(x), y, half(s(z)))) [1]

The TRS has the following type information:
check :: 0:s -> zero:odd:even
0 :: 0:s
zero :: zero:odd:even
s :: 0:s -> 0:s
odd :: zero:odd:even
even :: zero:odd:even
half :: 0:s -> 0:s
plus :: 0:s -> 0:s -> 0:s
times :: 0:s -> 0:s -> 0:s
timesIter :: 0:s -> 0:s -> 0:s -> 0:s
if :: zero:odd:even -> 0:s -> 0:s -> 0:s -> 0:s -> 0:s
p :: 0:s -> 0:s

Rewrite Strategy: INNERMOST
----------------------------------------

(11) NarrowingProof (BOTH BOUNDS(ID, ID))
Narrowed the inner basic terms of all right-hand sides by a single narrowing step.
----------------------------------------

(12)
Obligation:
Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is:

Runtime Complexity Weighted TRS with Types.
The TRS R consists of the following rules:

   check(0) -> zero [1]
   check(s(0)) -> odd [1]
   check(s(s(0))) -> even [1]
   check(s(s(s(x)))) -> check(s(x)) [1]
   half(0) -> 0 [1]
   half(s(0)) -> 0 [1]
   half(s(s(x))) -> s(half(x)) [1]
   plus(0, y) -> y [1]
   plus(s(x), y) -> s(plus(x, y)) [1]
   times(x, y) -> timesIter(x, y, 0) [1]
   timesIter(0, y, 0) -> if(zero, 0, y, 0, y) [3]
   timesIter(0, y, s(x'')) -> if(zero, 0, y, s(x''), s(plus(x'', y))) [3]
   timesIter(s(0), y, 0) -> if(odd, s(0), y, 0, y) [3]
   timesIter(s(0), y, s(x1)) -> if(odd, s(0), y, s(x1), s(plus(x1, y))) [3]
   timesIter(s(s(0)), y, 0) -> if(even, s(s(0)), y, 0, y) [3]
   timesIter(s(s(0)), y, s(x2)) -> if(even, s(s(0)), y, s(x2), s(plus(x2, y))) [3]
   timesIter(s(s(s(x'))), y, 0) -> if(check(s(x')), s(s(s(x'))), y, 0, y) [3]
   timesIter(s(s(s(x'))), y, s(x3)) -> if(check(s(x')), s(s(s(x'))), y, s(x3), s(plus(x3, y))) [3]
   p(s(x)) -> x [1]
   p(0) -> 0 [1]
   if(zero, x, y, z, u) -> z [1]
   if(odd, s(x4), y, z, u) -> timesIter(x4, y, u) [2]
   if(odd, 0, y, z, u) -> timesIter(0, y, u) [2]
   if(even, 0, y, 0, u) -> plus(timesIter(0, y, 0), timesIter(0, y, 0)) [5]
   if(even, 0, y, s(0), u) -> plus(timesIter(0, y, 0), timesIter(0, y, s(half(0)))) [5]
   if(even, 0, y, s(s(x6)), u) -> plus(timesIter(0, y, s(half(x6))), timesIter(0, y, s(half(s(x6))))) [5]
   if(even, s(0), y, 0, u) -> plus(timesIter(0, y, 0), timesIter(0, y, 0)) [5]
   if(even, s(0), y, s(0), u) -> plus(timesIter(0, y, 0), timesIter(0, y, s(half(0)))) [5]
   if(even, s(0), y, s(s(x7)), u) -> plus(timesIter(0, y, s(half(x7))), timesIter(0, y, s(half(s(x7))))) [5]
   if(even, s(s(x5)), y, 0, u) -> plus(timesIter(s(half(x5)), y, 0), timesIter(s(half(x5)), y, 0)) [5]
   if(even, s(s(x5)), y, s(0), u) -> plus(timesIter(s(half(x5)), y, 0), timesIter(s(half(x5)), y, s(half(0)))) [5]
   if(even, s(s(x5)), y, s(s(x8)), u) -> plus(timesIter(s(half(x5)), y, s(half(x8))), timesIter(s(half(x5)), y, s(half(s(x8))))) [5]

The TRS has the following type information:
check :: 0:s -> zero:odd:even
0 :: 0:s
zero :: zero:odd:even
s :: 0:s -> 0:s
odd :: zero:odd:even
even :: zero:odd:even
half :: 0:s -> 0:s
plus :: 0:s -> 0:s -> 0:s
times :: 0:s -> 0:s -> 0:s
timesIter :: 0:s -> 0:s -> 0:s -> 0:s
if :: zero:odd:even -> 0:s -> 0:s -> 0:s -> 0:s -> 0:s
p :: 0:s -> 0:s

Rewrite Strategy: INNERMOST
----------------------------------------

(13) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID))
Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction.
The constant constructors are abstracted as follows:

   0 => 0
   zero => 2
   odd => 1
   even => 0

----------------------------------------

(14)
Obligation:
Complexity RNTS consisting of the following rules:

   check(z') -{ 1 }-> check(1 + x) :|: x >= 0, z' = 1 + (1 + (1 + x))
   check(z') -{ 1 }-> 2 :|: z' = 0
   check(z') -{ 1 }-> 1 :|: z' = 1 + 0
   check(z') -{ 1 }-> 0 :|: z' = 1 + (1 + 0)
   half(z') -{ 1 }-> 0 :|: z' = 0
   half(z') -{ 1 }-> 0 :|: z' = 1 + 0
   half(z') -{ 1 }-> 1 + half(x) :|: x >= 0, z' = 1 + (1 + x)
   if(z', z'', z1, z2, z3) -{ 1 }-> z :|: z1 = y, z >= 0, z' = 2, z2 = z, x >= 0, y >= 0, z'' = x, z3 = u, u >= 0
   if(z', z'', z1, z2, z3) -{ 2 }-> timesIter(x4, y, u) :|: z1 = y, x4 >= 0, z >= 0, z'' = 1 + x4, z2 = z, y >= 0, z' = 1, z3 = u, u >= 0
   if(z', z'', z1, z2, z3) -{ 2 }-> timesIter(0, y, u) :|: z'' = 0, z1 = y, z >= 0, z2 = z, y >= 0, z' = 1, z3 = u, u >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, y, 0), timesIter(0, y, 0)) :|: z'' = 0, z1 = y, z2 = 0, y >= 0, z3 = u, z' = 0, u >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, y, 0), timesIter(0, y, 0)) :|: z1 = y, z2 = 0, y >= 0, z'' = 1 + 0, z3 = u, z' = 0, u >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, y, 0), timesIter(0, y, 1 + half(0))) :|: z'' = 0, z1 = y, z2 = 1 + 0, y >= 0, z3 = u, z' = 0, u >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, y, 0), timesIter(0, y, 1 + half(0))) :|: z1 = y, z2 = 1 + 0, y >= 0, z'' = 1 + 0, z3 = u, z' = 0, u >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, y, 1 + half(x6)), timesIter(0, y, 1 + half(1 + x6))) :|: z'' = 0, z1 = y, y >= 0, x6 >= 0, z2 = 1 + (1 + x6), z3 = u, z' = 0, u >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, y, 1 + half(x7)), timesIter(0, y, 1 + half(1 + x7))) :|: z1 = y, x7 >= 0, y >= 0, z'' = 1 + 0, z3 = u, z' = 0, z2 = 1 + (1 + x7), u >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(1 + half(x5), y, 0), timesIter(1 + half(x5), y, 0)) :|: z1 = y, x5 >= 0, z2 = 0, y >= 0, z'' = 1 + (1 + x5), z3 = u, z' = 0, u >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(1 + half(x5), y, 0), timesIter(1 + half(x5), y, 1 + half(0))) :|: z1 = y, z2 = 1 + 0, x5 >= 0, y >= 0, z'' = 1 + (1 + x5), z3 = u, z' = 0, u >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(1 + half(x5), y, 1 + half(x8)), timesIter(1 + half(x5), y, 1 + half(1 + x8))) :|: z1 = y, x5 >= 0, x8 >= 0, y >= 0, z2 = 1 + (1 + x8), z'' = 1 + (1 + x5), z3 = u, z' = 0, u >= 0
   p(z') -{ 1 }-> x :|: z' = 1 + x, x >= 0
   p(z') -{ 1 }-> 0 :|: z' = 0
   plus(z', z'') -{ 1 }-> y :|: z'' = y, y >= 0, z' = 0
   plus(z', z'') -{ 1 }-> 1 + plus(x, y) :|: z' = 1 + x, z'' = y, x >= 0, y >= 0
   times(z', z'') -{ 1 }-> timesIter(x, y, 0) :|: z' = x, z'' = y, x >= 0, y >= 0
   timesIter(z', z'', z1) -{ 3 }-> if(check(1 + x'), 1 + (1 + (1 + x')), y, 0, y) :|: z' = 1 + (1 + (1 + x')), z1 = 0, z'' = y, x' >= 0, y >= 0
   timesIter(z', z'', z1) -{ 3 }-> if(check(1 + x'), 1 + (1 + (1 + x')), y, 1 + x3, 1 + plus(x3, y)) :|: z' = 1 + (1 + (1 + x')), z'' = y, x' >= 0, y >= 0, z1 = 1 + x3, x3 >= 0
   timesIter(z', z'', z1) -{ 3 }-> if(2, 0, y, 0, y) :|: z1 = 0, z'' = y, y >= 0, z' = 0
   timesIter(z', z'', z1) -{ 3 }-> if(2, 0, y, 1 + x'', 1 + plus(x'', y)) :|: z1 = 1 + x'', z'' = y, y >= 0, x'' >= 0, z' = 0
   timesIter(z', z'', z1) -{ 3 }-> if(1, 1 + 0, y, 0, y) :|: z1 = 0, z'' = y, y >= 0, z' = 1 + 0
   timesIter(z', z'', z1) -{ 3 }-> if(1, 1 + 0, y, 1 + x1, 1 + plus(x1, y)) :|: x1 >= 0, z'' = y, y >= 0, z' = 1 + 0, z1 = 1 + x1
   timesIter(z', z'', z1) -{ 3 }-> if(0, 1 + (1 + 0), y, 0, y) :|: z1 = 0, z' = 1 + (1 + 0), z'' = y, y >= 0
   timesIter(z', z'', z1) -{ 3 }-> if(0, 1 + (1 + 0), y, 1 + x2, 1 + plus(x2, y)) :|: z' = 1 + (1 + 0), z'' = y, y >= 0, x2 >= 0, z1 = 1 + x2


----------------------------------------

(15) SimplificationProof (BOTH BOUNDS(ID, ID))
Simplified the RNTS by moving equalities from the constraints into the right-hand sides.
----------------------------------------

(16)
Obligation:
Complexity RNTS consisting of the following rules:

   check(z') -{ 1 }-> check(1 + (z' - 3)) :|: z' - 3 >= 0
   check(z') -{ 1 }-> 2 :|: z' = 0
   check(z') -{ 1 }-> 1 :|: z' = 1 + 0
   check(z') -{ 1 }-> 0 :|: z' = 1 + (1 + 0)
   half(z') -{ 1 }-> 0 :|: z' = 0
   half(z') -{ 1 }-> 0 :|: z' = 1 + 0
   half(z') -{ 1 }-> 1 + half(z' - 2) :|: z' - 2 >= 0
   if(z', z'', z1, z2, z3) -{ 1 }-> z2 :|: z2 >= 0, z' = 2, z'' >= 0, z1 >= 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 2 }-> timesIter(0, z1, z3) :|: z'' = 0, z2 >= 0, z1 >= 0, z' = 1, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 2 }-> timesIter(z'' - 1, z1, z3) :|: z'' - 1 >= 0, z2 >= 0, z1 >= 0, z' = 1, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 0)) :|: z'' = 0, z2 = 0, z1 >= 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 0)) :|: z2 = 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 1 + half(0))) :|: z'' = 0, z2 = 1 + 0, z1 >= 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 1 + half(0))) :|: z2 = 1 + 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 1 + half(z2 - 2)), timesIter(0, z1, 1 + half(1 + (z2 - 2)))) :|: z'' = 0, z1 >= 0, z2 - 2 >= 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 1 + half(z2 - 2)), timesIter(0, z1, 1 + half(1 + (z2 - 2)))) :|: z2 - 2 >= 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(1 + half(z'' - 2), z1, 0), timesIter(1 + half(z'' - 2), z1, 0)) :|: z'' - 2 >= 0, z2 = 0, z1 >= 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(1 + half(z'' - 2), z1, 0), timesIter(1 + half(z'' - 2), z1, 1 + half(0))) :|: z2 = 1 + 0, z'' - 2 >= 0, z1 >= 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(1 + half(z'' - 2), z1, 1 + half(z2 - 2)), timesIter(1 + half(z'' - 2), z1, 1 + half(1 + (z2 - 2)))) :|: z'' - 2 >= 0, z2 - 2 >= 0, z1 >= 0, z' = 0, z3 >= 0
   p(z') -{ 1 }-> 0 :|: z' = 0
   p(z') -{ 1 }-> z' - 1 :|: z' - 1 >= 0
   plus(z', z'') -{ 1 }-> z'' :|: z'' >= 0, z' = 0
   plus(z', z'') -{ 1 }-> 1 + plus(z' - 1, z'') :|: z' - 1 >= 0, z'' >= 0
   times(z', z'') -{ 1 }-> timesIter(z', z'', 0) :|: z' >= 0, z'' >= 0
   timesIter(z', z'', z1) -{ 3 }-> if(check(1 + (z' - 3)), 1 + (1 + (1 + (z' - 3))), z'', 0, z'') :|: z1 = 0, z' - 3 >= 0, z'' >= 0
   timesIter(z', z'', z1) -{ 3 }-> if(check(1 + (z' - 3)), 1 + (1 + (1 + (z' - 3))), z'', 1 + (z1 - 1), 1 + plus(z1 - 1, z'')) :|: z' - 3 >= 0, z'' >= 0, z1 - 1 >= 0
   timesIter(z', z'', z1) -{ 3 }-> if(2, 0, z'', 0, z'') :|: z1 = 0, z'' >= 0, z' = 0
   timesIter(z', z'', z1) -{ 3 }-> if(2, 0, z'', 1 + (z1 - 1), 1 + plus(z1 - 1, z'')) :|: z'' >= 0, z1 - 1 >= 0, z' = 0
   timesIter(z', z'', z1) -{ 3 }-> if(1, 1 + 0, z'', 0, z'') :|: z1 = 0, z'' >= 0, z' = 1 + 0
   timesIter(z', z'', z1) -{ 3 }-> if(1, 1 + 0, z'', 1 + (z1 - 1), 1 + plus(z1 - 1, z'')) :|: z1 - 1 >= 0, z'' >= 0, z' = 1 + 0
   timesIter(z', z'', z1) -{ 3 }-> if(0, 1 + (1 + 0), z'', 0, z'') :|: z1 = 0, z' = 1 + (1 + 0), z'' >= 0
   timesIter(z', z'', z1) -{ 3 }-> if(0, 1 + (1 + 0), z'', 1 + (z1 - 1), 1 + plus(z1 - 1, z'')) :|: z' = 1 + (1 + 0), z'' >= 0, z1 - 1 >= 0


----------------------------------------

(17) CpxRntsAnalysisOrderProof (BOTH BOUNDS(ID, ID))
Found the following analysis order by SCC decomposition:

   { check }
   { half }
   { plus }
   { p }
   { timesIter, if }
   { times }

----------------------------------------

(18)
Obligation:
Complexity RNTS consisting of the following rules:

   check(z') -{ 1 }-> check(1 + (z' - 3)) :|: z' - 3 >= 0
   check(z') -{ 1 }-> 2 :|: z' = 0
   check(z') -{ 1 }-> 1 :|: z' = 1 + 0
   check(z') -{ 1 }-> 0 :|: z' = 1 + (1 + 0)
   half(z') -{ 1 }-> 0 :|: z' = 0
   half(z') -{ 1 }-> 0 :|: z' = 1 + 0
   half(z') -{ 1 }-> 1 + half(z' - 2) :|: z' - 2 >= 0
   if(z', z'', z1, z2, z3) -{ 1 }-> z2 :|: z2 >= 0, z' = 2, z'' >= 0, z1 >= 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 2 }-> timesIter(0, z1, z3) :|: z'' = 0, z2 >= 0, z1 >= 0, z' = 1, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 2 }-> timesIter(z'' - 1, z1, z3) :|: z'' - 1 >= 0, z2 >= 0, z1 >= 0, z' = 1, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 0)) :|: z'' = 0, z2 = 0, z1 >= 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 0)) :|: z2 = 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 1 + half(0))) :|: z'' = 0, z2 = 1 + 0, z1 >= 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 1 + half(0))) :|: z2 = 1 + 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 1 + half(z2 - 2)), timesIter(0, z1, 1 + half(1 + (z2 - 2)))) :|: z'' = 0, z1 >= 0, z2 - 2 >= 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 1 + half(z2 - 2)), timesIter(0, z1, 1 + half(1 + (z2 - 2)))) :|: z2 - 2 >= 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(1 + half(z'' - 2), z1, 0), timesIter(1 + half(z'' - 2), z1, 0)) :|: z'' - 2 >= 0, z2 = 0, z1 >= 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(1 + half(z'' - 2), z1, 0), timesIter(1 + half(z'' - 2), z1, 1 + half(0))) :|: z2 = 1 + 0, z'' - 2 >= 0, z1 >= 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(1 + half(z'' - 2), z1, 1 + half(z2 - 2)), timesIter(1 + half(z'' - 2), z1, 1 + half(1 + (z2 - 2)))) :|: z'' - 2 >= 0, z2 - 2 >= 0, z1 >= 0, z' = 0, z3 >= 0
   p(z') -{ 1 }-> 0 :|: z' = 0
   p(z') -{ 1 }-> z' - 1 :|: z' - 1 >= 0
   plus(z', z'') -{ 1 }-> z'' :|: z'' >= 0, z' = 0
   plus(z', z'') -{ 1 }-> 1 + plus(z' - 1, z'') :|: z' - 1 >= 0, z'' >= 0
   times(z', z'') -{ 1 }-> timesIter(z', z'', 0) :|: z' >= 0, z'' >= 0
   timesIter(z', z'', z1) -{ 3 }-> if(check(1 + (z' - 3)), 1 + (1 + (1 + (z' - 3))), z'', 0, z'') :|: z1 = 0, z' - 3 >= 0, z'' >= 0
   timesIter(z', z'', z1) -{ 3 }-> if(check(1 + (z' - 3)), 1 + (1 + (1 + (z' - 3))), z'', 1 + (z1 - 1), 1 + plus(z1 - 1, z'')) :|: z' - 3 >= 0, z'' >= 0, z1 - 1 >= 0
   timesIter(z', z'', z1) -{ 3 }-> if(2, 0, z'', 0, z'') :|: z1 = 0, z'' >= 0, z' = 0
   timesIter(z', z'', z1) -{ 3 }-> if(2, 0, z'', 1 + (z1 - 1), 1 + plus(z1 - 1, z'')) :|: z'' >= 0, z1 - 1 >= 0, z' = 0
   timesIter(z', z'', z1) -{ 3 }-> if(1, 1 + 0, z'', 0, z'') :|: z1 = 0, z'' >= 0, z' = 1 + 0
   timesIter(z', z'', z1) -{ 3 }-> if(1, 1 + 0, z'', 1 + (z1 - 1), 1 + plus(z1 - 1, z'')) :|: z1 - 1 >= 0, z'' >= 0, z' = 1 + 0
   timesIter(z', z'', z1) -{ 3 }-> if(0, 1 + (1 + 0), z'', 0, z'') :|: z1 = 0, z' = 1 + (1 + 0), z'' >= 0
   timesIter(z', z'', z1) -{ 3 }-> if(0, 1 + (1 + 0), z'', 1 + (z1 - 1), 1 + plus(z1 - 1, z'')) :|: z' = 1 + (1 + 0), z'' >= 0, z1 - 1 >= 0

Function symbols to be analyzed: {check}, {half}, {plus}, {p}, {timesIter,if}, {times}

----------------------------------------

(19) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

(20)
Obligation:
Complexity RNTS consisting of the following rules:

   check(z') -{ 1 }-> check(1 + (z' - 3)) :|: z' - 3 >= 0
   check(z') -{ 1 }-> 2 :|: z' = 0
   check(z') -{ 1 }-> 1 :|: z' = 1 + 0
   check(z') -{ 1 }-> 0 :|: z' = 1 + (1 + 0)
   half(z') -{ 1 }-> 0 :|: z' = 0
   half(z') -{ 1 }-> 0 :|: z' = 1 + 0
   half(z') -{ 1 }-> 1 + half(z' - 2) :|: z' - 2 >= 0
   if(z', z'', z1, z2, z3) -{ 1 }-> z2 :|: z2 >= 0, z' = 2, z'' >= 0, z1 >= 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 2 }-> timesIter(0, z1, z3) :|: z'' = 0, z2 >= 0, z1 >= 0, z' = 1, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 2 }-> timesIter(z'' - 1, z1, z3) :|: z'' - 1 >= 0, z2 >= 0, z1 >= 0, z' = 1, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 0)) :|: z'' = 0, z2 = 0, z1 >= 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 0)) :|: z2 = 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 1 + half(0))) :|: z'' = 0, z2 = 1 + 0, z1 >= 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 1 + half(0))) :|: z2 = 1 + 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 1 + half(z2 - 2)), timesIter(0, z1, 1 + half(1 + (z2 - 2)))) :|: z'' = 0, z1 >= 0, z2 - 2 >= 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 1 + half(z2 - 2)), timesIter(0, z1, 1 + half(1 + (z2 - 2)))) :|: z2 - 2 >= 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(1 + half(z'' - 2), z1, 0), timesIter(1 + half(z'' - 2), z1, 0)) :|: z'' - 2 >= 0, z2 = 0, z1 >= 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(1 + half(z'' - 2), z1, 0), timesIter(1 + half(z'' - 2), z1, 1 + half(0))) :|: z2 = 1 + 0, z'' - 2 >= 0, z1 >= 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(1 + half(z'' - 2), z1, 1 + half(z2 - 2)), timesIter(1 + half(z'' - 2), z1, 1 + half(1 + (z2 - 2)))) :|: z'' - 2 >= 0, z2 - 2 >= 0, z1 >= 0, z' = 0, z3 >= 0
   p(z') -{ 1 }-> 0 :|: z' = 0
   p(z') -{ 1 }-> z' - 1 :|: z' - 1 >= 0
   plus(z', z'') -{ 1 }-> z'' :|: z'' >= 0, z' = 0
   plus(z', z'') -{ 1 }-> 1 + plus(z' - 1, z'') :|: z' - 1 >= 0, z'' >= 0
   times(z', z'') -{ 1 }-> timesIter(z', z'', 0) :|: z' >= 0, z'' >= 0
   timesIter(z', z'', z1) -{ 3 }-> if(check(1 + (z' - 3)), 1 + (1 + (1 + (z' - 3))), z'', 0, z'') :|: z1 = 0, z' - 3 >= 0, z'' >= 0
   timesIter(z', z'', z1) -{ 3 }-> if(check(1 + (z' - 3)), 1 + (1 + (1 + (z' - 3))), z'', 1 + (z1 - 1), 1 + plus(z1 - 1, z'')) :|: z' - 3 >= 0, z'' >= 0, z1 - 1 >= 0
   timesIter(z', z'', z1) -{ 3 }-> if(2, 0, z'', 0, z'') :|: z1 = 0, z'' >= 0, z' = 0
   timesIter(z', z'', z1) -{ 3 }-> if(2, 0, z'', 1 + (z1 - 1), 1 + plus(z1 - 1, z'')) :|: z'' >= 0, z1 - 1 >= 0, z' = 0
   timesIter(z', z'', z1) -{ 3 }-> if(1, 1 + 0, z'', 0, z'') :|: z1 = 0, z'' >= 0, z' = 1 + 0
   timesIter(z', z'', z1) -{ 3 }-> if(1, 1 + 0, z'', 1 + (z1 - 1), 1 + plus(z1 - 1, z'')) :|: z1 - 1 >= 0, z'' >= 0, z' = 1 + 0
   timesIter(z', z'', z1) -{ 3 }-> if(0, 1 + (1 + 0), z'', 0, z'') :|: z1 = 0, z' = 1 + (1 + 0), z'' >= 0
   timesIter(z', z'', z1) -{ 3 }-> if(0, 1 + (1 + 0), z'', 1 + (z1 - 1), 1 + plus(z1 - 1, z'')) :|: z' = 1 + (1 + 0), z'' >= 0, z1 - 1 >= 0

Function symbols to be analyzed: {check}, {half}, {plus}, {p}, {timesIter,if}, {times}

----------------------------------------

(21) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: check
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 2

----------------------------------------

(22)
Obligation:
Complexity RNTS consisting of the following rules:

   check(z') -{ 1 }-> check(1 + (z' - 3)) :|: z' - 3 >= 0
   check(z') -{ 1 }-> 2 :|: z' = 0
   check(z') -{ 1 }-> 1 :|: z' = 1 + 0
   check(z') -{ 1 }-> 0 :|: z' = 1 + (1 + 0)
   half(z') -{ 1 }-> 0 :|: z' = 0
   half(z') -{ 1 }-> 0 :|: z' = 1 + 0
   half(z') -{ 1 }-> 1 + half(z' - 2) :|: z' - 2 >= 0
   if(z', z'', z1, z2, z3) -{ 1 }-> z2 :|: z2 >= 0, z' = 2, z'' >= 0, z1 >= 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 2 }-> timesIter(0, z1, z3) :|: z'' = 0, z2 >= 0, z1 >= 0, z' = 1, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 2 }-> timesIter(z'' - 1, z1, z3) :|: z'' - 1 >= 0, z2 >= 0, z1 >= 0, z' = 1, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 0)) :|: z'' = 0, z2 = 0, z1 >= 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 0)) :|: z2 = 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 1 + half(0))) :|: z'' = 0, z2 = 1 + 0, z1 >= 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 1 + half(0))) :|: z2 = 1 + 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 1 + half(z2 - 2)), timesIter(0, z1, 1 + half(1 + (z2 - 2)))) :|: z'' = 0, z1 >= 0, z2 - 2 >= 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 1 + half(z2 - 2)), timesIter(0, z1, 1 + half(1 + (z2 - 2)))) :|: z2 - 2 >= 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(1 + half(z'' - 2), z1, 0), timesIter(1 + half(z'' - 2), z1, 0)) :|: z'' - 2 >= 0, z2 = 0, z1 >= 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(1 + half(z'' - 2), z1, 0), timesIter(1 + half(z'' - 2), z1, 1 + half(0))) :|: z2 = 1 + 0, z'' - 2 >= 0, z1 >= 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(1 + half(z'' - 2), z1, 1 + half(z2 - 2)), timesIter(1 + half(z'' - 2), z1, 1 + half(1 + (z2 - 2)))) :|: z'' - 2 >= 0, z2 - 2 >= 0, z1 >= 0, z' = 0, z3 >= 0
   p(z') -{ 1 }-> 0 :|: z' = 0
   p(z') -{ 1 }-> z' - 1 :|: z' - 1 >= 0
   plus(z', z'') -{ 1 }-> z'' :|: z'' >= 0, z' = 0
   plus(z', z'') -{ 1 }-> 1 + plus(z' - 1, z'') :|: z' - 1 >= 0, z'' >= 0
   times(z', z'') -{ 1 }-> timesIter(z', z'', 0) :|: z' >= 0, z'' >= 0
   timesIter(z', z'', z1) -{ 3 }-> if(check(1 + (z' - 3)), 1 + (1 + (1 + (z' - 3))), z'', 0, z'') :|: z1 = 0, z' - 3 >= 0, z'' >= 0
   timesIter(z', z'', z1) -{ 3 }-> if(check(1 + (z' - 3)), 1 + (1 + (1 + (z' - 3))), z'', 1 + (z1 - 1), 1 + plus(z1 - 1, z'')) :|: z' - 3 >= 0, z'' >= 0, z1 - 1 >= 0
   timesIter(z', z'', z1) -{ 3 }-> if(2, 0, z'', 0, z'') :|: z1 = 0, z'' >= 0, z' = 0
   timesIter(z', z'', z1) -{ 3 }-> if(2, 0, z'', 1 + (z1 - 1), 1 + plus(z1 - 1, z'')) :|: z'' >= 0, z1 - 1 >= 0, z' = 0
   timesIter(z', z'', z1) -{ 3 }-> if(1, 1 + 0, z'', 0, z'') :|: z1 = 0, z'' >= 0, z' = 1 + 0
   timesIter(z', z'', z1) -{ 3 }-> if(1, 1 + 0, z'', 1 + (z1 - 1), 1 + plus(z1 - 1, z'')) :|: z1 - 1 >= 0, z'' >= 0, z' = 1 + 0
   timesIter(z', z'', z1) -{ 3 }-> if(0, 1 + (1 + 0), z'', 0, z'') :|: z1 = 0, z' = 1 + (1 + 0), z'' >= 0
   timesIter(z', z'', z1) -{ 3 }-> if(0, 1 + (1 + 0), z'', 1 + (z1 - 1), 1 + plus(z1 - 1, z'')) :|: z' = 1 + (1 + 0), z'' >= 0, z1 - 1 >= 0

Function symbols to be analyzed: {check}, {half}, {plus}, {p}, {timesIter,if}, {times}
Previous analysis results are:
  check: runtime: ?, size: O(1) [2]

----------------------------------------

(23) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: check
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 2 + z'

----------------------------------------

(24)
Obligation:
Complexity RNTS consisting of the following rules:

   check(z') -{ 1 }-> check(1 + (z' - 3)) :|: z' - 3 >= 0
   check(z') -{ 1 }-> 2 :|: z' = 0
   check(z') -{ 1 }-> 1 :|: z' = 1 + 0
   check(z') -{ 1 }-> 0 :|: z' = 1 + (1 + 0)
   half(z') -{ 1 }-> 0 :|: z' = 0
   half(z') -{ 1 }-> 0 :|: z' = 1 + 0
   half(z') -{ 1 }-> 1 + half(z' - 2) :|: z' - 2 >= 0
   if(z', z'', z1, z2, z3) -{ 1 }-> z2 :|: z2 >= 0, z' = 2, z'' >= 0, z1 >= 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 2 }-> timesIter(0, z1, z3) :|: z'' = 0, z2 >= 0, z1 >= 0, z' = 1, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 2 }-> timesIter(z'' - 1, z1, z3) :|: z'' - 1 >= 0, z2 >= 0, z1 >= 0, z' = 1, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 0)) :|: z'' = 0, z2 = 0, z1 >= 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 0)) :|: z2 = 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 1 + half(0))) :|: z'' = 0, z2 = 1 + 0, z1 >= 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 1 + half(0))) :|: z2 = 1 + 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 1 + half(z2 - 2)), timesIter(0, z1, 1 + half(1 + (z2 - 2)))) :|: z'' = 0, z1 >= 0, z2 - 2 >= 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 1 + half(z2 - 2)), timesIter(0, z1, 1 + half(1 + (z2 - 2)))) :|: z2 - 2 >= 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(1 + half(z'' - 2), z1, 0), timesIter(1 + half(z'' - 2), z1, 0)) :|: z'' - 2 >= 0, z2 = 0, z1 >= 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(1 + half(z'' - 2), z1, 0), timesIter(1 + half(z'' - 2), z1, 1 + half(0))) :|: z2 = 1 + 0, z'' - 2 >= 0, z1 >= 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(1 + half(z'' - 2), z1, 1 + half(z2 - 2)), timesIter(1 + half(z'' - 2), z1, 1 + half(1 + (z2 - 2)))) :|: z'' - 2 >= 0, z2 - 2 >= 0, z1 >= 0, z' = 0, z3 >= 0
   p(z') -{ 1 }-> 0 :|: z' = 0
   p(z') -{ 1 }-> z' - 1 :|: z' - 1 >= 0
   plus(z', z'') -{ 1 }-> z'' :|: z'' >= 0, z' = 0
   plus(z', z'') -{ 1 }-> 1 + plus(z' - 1, z'') :|: z' - 1 >= 0, z'' >= 0
   times(z', z'') -{ 1 }-> timesIter(z', z'', 0) :|: z' >= 0, z'' >= 0
   timesIter(z', z'', z1) -{ 3 }-> if(check(1 + (z' - 3)), 1 + (1 + (1 + (z' - 3))), z'', 0, z'') :|: z1 = 0, z' - 3 >= 0, z'' >= 0
   timesIter(z', z'', z1) -{ 3 }-> if(check(1 + (z' - 3)), 1 + (1 + (1 + (z' - 3))), z'', 1 + (z1 - 1), 1 + plus(z1 - 1, z'')) :|: z' - 3 >= 0, z'' >= 0, z1 - 1 >= 0
   timesIter(z', z'', z1) -{ 3 }-> if(2, 0, z'', 0, z'') :|: z1 = 0, z'' >= 0, z' = 0
   timesIter(z', z'', z1) -{ 3 }-> if(2, 0, z'', 1 + (z1 - 1), 1 + plus(z1 - 1, z'')) :|: z'' >= 0, z1 - 1 >= 0, z' = 0
   timesIter(z', z'', z1) -{ 3 }-> if(1, 1 + 0, z'', 0, z'') :|: z1 = 0, z'' >= 0, z' = 1 + 0
   timesIter(z', z'', z1) -{ 3 }-> if(1, 1 + 0, z'', 1 + (z1 - 1), 1 + plus(z1 - 1, z'')) :|: z1 - 1 >= 0, z'' >= 0, z' = 1 + 0
   timesIter(z', z'', z1) -{ 3 }-> if(0, 1 + (1 + 0), z'', 0, z'') :|: z1 = 0, z' = 1 + (1 + 0), z'' >= 0
   timesIter(z', z'', z1) -{ 3 }-> if(0, 1 + (1 + 0), z'', 1 + (z1 - 1), 1 + plus(z1 - 1, z'')) :|: z' = 1 + (1 + 0), z'' >= 0, z1 - 1 >= 0

Function symbols to be analyzed: {half}, {plus}, {p}, {timesIter,if}, {times}
Previous analysis results are:
  check: runtime: O(n^1) [2 + z'], size: O(1) [2]

----------------------------------------

(25) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

(26)
Obligation:
Complexity RNTS consisting of the following rules:

   check(z') -{ 1 + z' }-> s :|: s >= 0, s <= 2, z' - 3 >= 0
   check(z') -{ 1 }-> 2 :|: z' = 0
   check(z') -{ 1 }-> 1 :|: z' = 1 + 0
   check(z') -{ 1 }-> 0 :|: z' = 1 + (1 + 0)
   half(z') -{ 1 }-> 0 :|: z' = 0
   half(z') -{ 1 }-> 0 :|: z' = 1 + 0
   half(z') -{ 1 }-> 1 + half(z' - 2) :|: z' - 2 >= 0
   if(z', z'', z1, z2, z3) -{ 1 }-> z2 :|: z2 >= 0, z' = 2, z'' >= 0, z1 >= 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 2 }-> timesIter(0, z1, z3) :|: z'' = 0, z2 >= 0, z1 >= 0, z' = 1, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 2 }-> timesIter(z'' - 1, z1, z3) :|: z'' - 1 >= 0, z2 >= 0, z1 >= 0, z' = 1, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 0)) :|: z'' = 0, z2 = 0, z1 >= 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 0)) :|: z2 = 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 1 + half(0))) :|: z'' = 0, z2 = 1 + 0, z1 >= 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 1 + half(0))) :|: z2 = 1 + 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 1 + half(z2 - 2)), timesIter(0, z1, 1 + half(1 + (z2 - 2)))) :|: z'' = 0, z1 >= 0, z2 - 2 >= 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 1 + half(z2 - 2)), timesIter(0, z1, 1 + half(1 + (z2 - 2)))) :|: z2 - 2 >= 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(1 + half(z'' - 2), z1, 0), timesIter(1 + half(z'' - 2), z1, 0)) :|: z'' - 2 >= 0, z2 = 0, z1 >= 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(1 + half(z'' - 2), z1, 0), timesIter(1 + half(z'' - 2), z1, 1 + half(0))) :|: z2 = 1 + 0, z'' - 2 >= 0, z1 >= 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(1 + half(z'' - 2), z1, 1 + half(z2 - 2)), timesIter(1 + half(z'' - 2), z1, 1 + half(1 + (z2 - 2)))) :|: z'' - 2 >= 0, z2 - 2 >= 0, z1 >= 0, z' = 0, z3 >= 0
   p(z') -{ 1 }-> 0 :|: z' = 0
   p(z') -{ 1 }-> z' - 1 :|: z' - 1 >= 0
   plus(z', z'') -{ 1 }-> z'' :|: z'' >= 0, z' = 0
   plus(z', z'') -{ 1 }-> 1 + plus(z' - 1, z'') :|: z' - 1 >= 0, z'' >= 0
   times(z', z'') -{ 1 }-> timesIter(z', z'', 0) :|: z' >= 0, z'' >= 0
   timesIter(z', z'', z1) -{ 3 + z' }-> if(s', 1 + (1 + (1 + (z' - 3))), z'', 0, z'') :|: s' >= 0, s' <= 2, z1 = 0, z' - 3 >= 0, z'' >= 0
   timesIter(z', z'', z1) -{ 3 + z' }-> if(s'', 1 + (1 + (1 + (z' - 3))), z'', 1 + (z1 - 1), 1 + plus(z1 - 1, z'')) :|: s'' >= 0, s'' <= 2, z' - 3 >= 0, z'' >= 0, z1 - 1 >= 0
   timesIter(z', z'', z1) -{ 3 }-> if(2, 0, z'', 0, z'') :|: z1 = 0, z'' >= 0, z' = 0
   timesIter(z', z'', z1) -{ 3 }-> if(2, 0, z'', 1 + (z1 - 1), 1 + plus(z1 - 1, z'')) :|: z'' >= 0, z1 - 1 >= 0, z' = 0
   timesIter(z', z'', z1) -{ 3 }-> if(1, 1 + 0, z'', 0, z'') :|: z1 = 0, z'' >= 0, z' = 1 + 0
   timesIter(z', z'', z1) -{ 3 }-> if(1, 1 + 0, z'', 1 + (z1 - 1), 1 + plus(z1 - 1, z'')) :|: z1 - 1 >= 0, z'' >= 0, z' = 1 + 0
   timesIter(z', z'', z1) -{ 3 }-> if(0, 1 + (1 + 0), z'', 0, z'') :|: z1 = 0, z' = 1 + (1 + 0), z'' >= 0
   timesIter(z', z'', z1) -{ 3 }-> if(0, 1 + (1 + 0), z'', 1 + (z1 - 1), 1 + plus(z1 - 1, z'')) :|: z' = 1 + (1 + 0), z'' >= 0, z1 - 1 >= 0

Function symbols to be analyzed: {half}, {plus}, {p}, {timesIter,if}, {times}
Previous analysis results are:
  check: runtime: O(n^1) [2 + z'], size: O(1) [2]

----------------------------------------

(27) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using KoAT for: half
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: z'

----------------------------------------

(28)
Obligation:
Complexity RNTS consisting of the following rules:

   check(z') -{ 1 + z' }-> s :|: s >= 0, s <= 2, z' - 3 >= 0
   check(z') -{ 1 }-> 2 :|: z' = 0
   check(z') -{ 1 }-> 1 :|: z' = 1 + 0
   check(z') -{ 1 }-> 0 :|: z' = 1 + (1 + 0)
   half(z') -{ 1 }-> 0 :|: z' = 0
   half(z') -{ 1 }-> 0 :|: z' = 1 + 0
   half(z') -{ 1 }-> 1 + half(z' - 2) :|: z' - 2 >= 0
   if(z', z'', z1, z2, z3) -{ 1 }-> z2 :|: z2 >= 0, z' = 2, z'' >= 0, z1 >= 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 2 }-> timesIter(0, z1, z3) :|: z'' = 0, z2 >= 0, z1 >= 0, z' = 1, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 2 }-> timesIter(z'' - 1, z1, z3) :|: z'' - 1 >= 0, z2 >= 0, z1 >= 0, z' = 1, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 0)) :|: z'' = 0, z2 = 0, z1 >= 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 0)) :|: z2 = 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 1 + half(0))) :|: z'' = 0, z2 = 1 + 0, z1 >= 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 1 + half(0))) :|: z2 = 1 + 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 1 + half(z2 - 2)), timesIter(0, z1, 1 + half(1 + (z2 - 2)))) :|: z'' = 0, z1 >= 0, z2 - 2 >= 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 1 + half(z2 - 2)), timesIter(0, z1, 1 + half(1 + (z2 - 2)))) :|: z2 - 2 >= 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(1 + half(z'' - 2), z1, 0), timesIter(1 + half(z'' - 2), z1, 0)) :|: z'' - 2 >= 0, z2 = 0, z1 >= 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(1 + half(z'' - 2), z1, 0), timesIter(1 + half(z'' - 2), z1, 1 + half(0))) :|: z2 = 1 + 0, z'' - 2 >= 0, z1 >= 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(1 + half(z'' - 2), z1, 1 + half(z2 - 2)), timesIter(1 + half(z'' - 2), z1, 1 + half(1 + (z2 - 2)))) :|: z'' - 2 >= 0, z2 - 2 >= 0, z1 >= 0, z' = 0, z3 >= 0
   p(z') -{ 1 }-> 0 :|: z' = 0
   p(z') -{ 1 }-> z' - 1 :|: z' - 1 >= 0
   plus(z', z'') -{ 1 }-> z'' :|: z'' >= 0, z' = 0
   plus(z', z'') -{ 1 }-> 1 + plus(z' - 1, z'') :|: z' - 1 >= 0, z'' >= 0
   times(z', z'') -{ 1 }-> timesIter(z', z'', 0) :|: z' >= 0, z'' >= 0
   timesIter(z', z'', z1) -{ 3 + z' }-> if(s', 1 + (1 + (1 + (z' - 3))), z'', 0, z'') :|: s' >= 0, s' <= 2, z1 = 0, z' - 3 >= 0, z'' >= 0
   timesIter(z', z'', z1) -{ 3 + z' }-> if(s'', 1 + (1 + (1 + (z' - 3))), z'', 1 + (z1 - 1), 1 + plus(z1 - 1, z'')) :|: s'' >= 0, s'' <= 2, z' - 3 >= 0, z'' >= 0, z1 - 1 >= 0
   timesIter(z', z'', z1) -{ 3 }-> if(2, 0, z'', 0, z'') :|: z1 = 0, z'' >= 0, z' = 0
   timesIter(z', z'', z1) -{ 3 }-> if(2, 0, z'', 1 + (z1 - 1), 1 + plus(z1 - 1, z'')) :|: z'' >= 0, z1 - 1 >= 0, z' = 0
   timesIter(z', z'', z1) -{ 3 }-> if(1, 1 + 0, z'', 0, z'') :|: z1 = 0, z'' >= 0, z' = 1 + 0
   timesIter(z', z'', z1) -{ 3 }-> if(1, 1 + 0, z'', 1 + (z1 - 1), 1 + plus(z1 - 1, z'')) :|: z1 - 1 >= 0, z'' >= 0, z' = 1 + 0
   timesIter(z', z'', z1) -{ 3 }-> if(0, 1 + (1 + 0), z'', 0, z'') :|: z1 = 0, z' = 1 + (1 + 0), z'' >= 0
   timesIter(z', z'', z1) -{ 3 }-> if(0, 1 + (1 + 0), z'', 1 + (z1 - 1), 1 + plus(z1 - 1, z'')) :|: z' = 1 + (1 + 0), z'' >= 0, z1 - 1 >= 0

Function symbols to be analyzed: {half}, {plus}, {p}, {timesIter,if}, {times}
Previous analysis results are:
  check: runtime: O(n^1) [2 + z'], size: O(1) [2]
  half: runtime: ?, size: O(n^1) [z']

----------------------------------------

(29) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: half
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 2 + z'

----------------------------------------

(30)
Obligation:
Complexity RNTS consisting of the following rules:

   check(z') -{ 1 + z' }-> s :|: s >= 0, s <= 2, z' - 3 >= 0
   check(z') -{ 1 }-> 2 :|: z' = 0
   check(z') -{ 1 }-> 1 :|: z' = 1 + 0
   check(z') -{ 1 }-> 0 :|: z' = 1 + (1 + 0)
   half(z') -{ 1 }-> 0 :|: z' = 0
   half(z') -{ 1 }-> 0 :|: z' = 1 + 0
   half(z') -{ 1 }-> 1 + half(z' - 2) :|: z' - 2 >= 0
   if(z', z'', z1, z2, z3) -{ 1 }-> z2 :|: z2 >= 0, z' = 2, z'' >= 0, z1 >= 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 2 }-> timesIter(0, z1, z3) :|: z'' = 0, z2 >= 0, z1 >= 0, z' = 1, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 2 }-> timesIter(z'' - 1, z1, z3) :|: z'' - 1 >= 0, z2 >= 0, z1 >= 0, z' = 1, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 0)) :|: z'' = 0, z2 = 0, z1 >= 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 0)) :|: z2 = 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 1 + half(0))) :|: z'' = 0, z2 = 1 + 0, z1 >= 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 1 + half(0))) :|: z2 = 1 + 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 1 + half(z2 - 2)), timesIter(0, z1, 1 + half(1 + (z2 - 2)))) :|: z'' = 0, z1 >= 0, z2 - 2 >= 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 1 + half(z2 - 2)), timesIter(0, z1, 1 + half(1 + (z2 - 2)))) :|: z2 - 2 >= 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(1 + half(z'' - 2), z1, 0), timesIter(1 + half(z'' - 2), z1, 0)) :|: z'' - 2 >= 0, z2 = 0, z1 >= 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(1 + half(z'' - 2), z1, 0), timesIter(1 + half(z'' - 2), z1, 1 + half(0))) :|: z2 = 1 + 0, z'' - 2 >= 0, z1 >= 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(1 + half(z'' - 2), z1, 1 + half(z2 - 2)), timesIter(1 + half(z'' - 2), z1, 1 + half(1 + (z2 - 2)))) :|: z'' - 2 >= 0, z2 - 2 >= 0, z1 >= 0, z' = 0, z3 >= 0
   p(z') -{ 1 }-> 0 :|: z' = 0
   p(z') -{ 1 }-> z' - 1 :|: z' - 1 >= 0
   plus(z', z'') -{ 1 }-> z'' :|: z'' >= 0, z' = 0
   plus(z', z'') -{ 1 }-> 1 + plus(z' - 1, z'') :|: z' - 1 >= 0, z'' >= 0
   times(z', z'') -{ 1 }-> timesIter(z', z'', 0) :|: z' >= 0, z'' >= 0
   timesIter(z', z'', z1) -{ 3 + z' }-> if(s', 1 + (1 + (1 + (z' - 3))), z'', 0, z'') :|: s' >= 0, s' <= 2, z1 = 0, z' - 3 >= 0, z'' >= 0
   timesIter(z', z'', z1) -{ 3 + z' }-> if(s'', 1 + (1 + (1 + (z' - 3))), z'', 1 + (z1 - 1), 1 + plus(z1 - 1, z'')) :|: s'' >= 0, s'' <= 2, z' - 3 >= 0, z'' >= 0, z1 - 1 >= 0
   timesIter(z', z'', z1) -{ 3 }-> if(2, 0, z'', 0, z'') :|: z1 = 0, z'' >= 0, z' = 0
   timesIter(z', z'', z1) -{ 3 }-> if(2, 0, z'', 1 + (z1 - 1), 1 + plus(z1 - 1, z'')) :|: z'' >= 0, z1 - 1 >= 0, z' = 0
   timesIter(z', z'', z1) -{ 3 }-> if(1, 1 + 0, z'', 0, z'') :|: z1 = 0, z'' >= 0, z' = 1 + 0
   timesIter(z', z'', z1) -{ 3 }-> if(1, 1 + 0, z'', 1 + (z1 - 1), 1 + plus(z1 - 1, z'')) :|: z1 - 1 >= 0, z'' >= 0, z' = 1 + 0
   timesIter(z', z'', z1) -{ 3 }-> if(0, 1 + (1 + 0), z'', 0, z'') :|: z1 = 0, z' = 1 + (1 + 0), z'' >= 0
   timesIter(z', z'', z1) -{ 3 }-> if(0, 1 + (1 + 0), z'', 1 + (z1 - 1), 1 + plus(z1 - 1, z'')) :|: z' = 1 + (1 + 0), z'' >= 0, z1 - 1 >= 0

Function symbols to be analyzed: {plus}, {p}, {timesIter,if}, {times}
Previous analysis results are:
  check: runtime: O(n^1) [2 + z'], size: O(1) [2]
  half: runtime: O(n^1) [2 + z'], size: O(n^1) [z']

----------------------------------------

(31) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

(32)
Obligation:
Complexity RNTS consisting of the following rules:

   check(z') -{ 1 + z' }-> s :|: s >= 0, s <= 2, z' - 3 >= 0
   check(z') -{ 1 }-> 2 :|: z' = 0
   check(z') -{ 1 }-> 1 :|: z' = 1 + 0
   check(z') -{ 1 }-> 0 :|: z' = 1 + (1 + 0)
   half(z') -{ 1 }-> 0 :|: z' = 0
   half(z') -{ 1 }-> 0 :|: z' = 1 + 0
   half(z') -{ 1 + z' }-> 1 + s1 :|: s1 >= 0, s1 <= z' - 2, z' - 2 >= 0
   if(z', z'', z1, z2, z3) -{ 1 }-> z2 :|: z2 >= 0, z' = 2, z'' >= 0, z1 >= 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 2 }-> timesIter(0, z1, z3) :|: z'' = 0, z2 >= 0, z1 >= 0, z' = 1, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 2 }-> timesIter(z'' - 1, z1, z3) :|: z'' - 1 >= 0, z2 >= 0, z1 >= 0, z' = 1, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 0)) :|: z'' = 0, z2 = 0, z1 >= 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 0)) :|: z2 = 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 7 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 1 + s2)) :|: s2 >= 0, s2 <= 0, z'' = 0, z2 = 1 + 0, z1 >= 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 7 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 1 + s5)) :|: s5 >= 0, s5 <= 0, z2 = 1 + 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 6 + 2*z2 }-> plus(timesIter(0, z1, 1 + s3), timesIter(0, z1, 1 + s4)) :|: s3 >= 0, s3 <= z2 - 2, s4 >= 0, s4 <= 1 + (z2 - 2), z'' = 0, z1 >= 0, z2 - 2 >= 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 6 + 2*z2 }-> plus(timesIter(0, z1, 1 + s6), timesIter(0, z1, 1 + s7)) :|: s6 >= 0, s6 <= z2 - 2, s7 >= 0, s7 <= 1 + (z2 - 2), z2 - 2 >= 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 7 + 2*z'' }-> plus(timesIter(1 + s10, z1, 0), timesIter(1 + s11, z1, 1 + s12)) :|: s10 >= 0, s10 <= z'' - 2, s11 >= 0, s11 <= z'' - 2, s12 >= 0, s12 <= 0, z2 = 1 + 0, z'' - 2 >= 0, z1 >= 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 6 + 2*z'' + 2*z2 }-> plus(timesIter(1 + s13, z1, 1 + s14), timesIter(1 + s15, z1, 1 + s16)) :|: s13 >= 0, s13 <= z'' - 2, s14 >= 0, s14 <= z2 - 2, s15 >= 0, s15 <= z'' - 2, s16 >= 0, s16 <= 1 + (z2 - 2), z'' - 2 >= 0, z2 - 2 >= 0, z1 >= 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 + 2*z'' }-> plus(timesIter(1 + s8, z1, 0), timesIter(1 + s9, z1, 0)) :|: s8 >= 0, s8 <= z'' - 2, s9 >= 0, s9 <= z'' - 2, z'' - 2 >= 0, z2 = 0, z1 >= 0, z' = 0, z3 >= 0
   p(z') -{ 1 }-> 0 :|: z' = 0
   p(z') -{ 1 }-> z' - 1 :|: z' - 1 >= 0
   plus(z', z'') -{ 1 }-> z'' :|: z'' >= 0, z' = 0
   plus(z', z'') -{ 1 }-> 1 + plus(z' - 1, z'') :|: z' - 1 >= 0, z'' >= 0
   times(z', z'') -{ 1 }-> timesIter(z', z'', 0) :|: z' >= 0, z'' >= 0
   timesIter(z', z'', z1) -{ 3 + z' }-> if(s', 1 + (1 + (1 + (z' - 3))), z'', 0, z'') :|: s' >= 0, s' <= 2, z1 = 0, z' - 3 >= 0, z'' >= 0
   timesIter(z', z'', z1) -{ 3 + z' }-> if(s'', 1 + (1 + (1 + (z' - 3))), z'', 1 + (z1 - 1), 1 + plus(z1 - 1, z'')) :|: s'' >= 0, s'' <= 2, z' - 3 >= 0, z'' >= 0, z1 - 1 >= 0
   timesIter(z', z'', z1) -{ 3 }-> if(2, 0, z'', 0, z'') :|: z1 = 0, z'' >= 0, z' = 0
   timesIter(z', z'', z1) -{ 3 }-> if(2, 0, z'', 1 + (z1 - 1), 1 + plus(z1 - 1, z'')) :|: z'' >= 0, z1 - 1 >= 0, z' = 0
   timesIter(z', z'', z1) -{ 3 }-> if(1, 1 + 0, z'', 0, z'') :|: z1 = 0, z'' >= 0, z' = 1 + 0
   timesIter(z', z'', z1) -{ 3 }-> if(1, 1 + 0, z'', 1 + (z1 - 1), 1 + plus(z1 - 1, z'')) :|: z1 - 1 >= 0, z'' >= 0, z' = 1 + 0
   timesIter(z', z'', z1) -{ 3 }-> if(0, 1 + (1 + 0), z'', 0, z'') :|: z1 = 0, z' = 1 + (1 + 0), z'' >= 0
   timesIter(z', z'', z1) -{ 3 }-> if(0, 1 + (1 + 0), z'', 1 + (z1 - 1), 1 + plus(z1 - 1, z'')) :|: z' = 1 + (1 + 0), z'' >= 0, z1 - 1 >= 0

Function symbols to be analyzed: {plus}, {p}, {timesIter,if}, {times}
Previous analysis results are:
  check: runtime: O(n^1) [2 + z'], size: O(1) [2]
  half: runtime: O(n^1) [2 + z'], size: O(n^1) [z']

----------------------------------------

(33) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: plus
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: z' + z''

----------------------------------------

(34)
Obligation:
Complexity RNTS consisting of the following rules:

   check(z') -{ 1 + z' }-> s :|: s >= 0, s <= 2, z' - 3 >= 0
   check(z') -{ 1 }-> 2 :|: z' = 0
   check(z') -{ 1 }-> 1 :|: z' = 1 + 0
   check(z') -{ 1 }-> 0 :|: z' = 1 + (1 + 0)
   half(z') -{ 1 }-> 0 :|: z' = 0
   half(z') -{ 1 }-> 0 :|: z' = 1 + 0
   half(z') -{ 1 + z' }-> 1 + s1 :|: s1 >= 0, s1 <= z' - 2, z' - 2 >= 0
   if(z', z'', z1, z2, z3) -{ 1 }-> z2 :|: z2 >= 0, z' = 2, z'' >= 0, z1 >= 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 2 }-> timesIter(0, z1, z3) :|: z'' = 0, z2 >= 0, z1 >= 0, z' = 1, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 2 }-> timesIter(z'' - 1, z1, z3) :|: z'' - 1 >= 0, z2 >= 0, z1 >= 0, z' = 1, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 0)) :|: z'' = 0, z2 = 0, z1 >= 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 0)) :|: z2 = 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 7 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 1 + s2)) :|: s2 >= 0, s2 <= 0, z'' = 0, z2 = 1 + 0, z1 >= 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 7 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 1 + s5)) :|: s5 >= 0, s5 <= 0, z2 = 1 + 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 6 + 2*z2 }-> plus(timesIter(0, z1, 1 + s3), timesIter(0, z1, 1 + s4)) :|: s3 >= 0, s3 <= z2 - 2, s4 >= 0, s4 <= 1 + (z2 - 2), z'' = 0, z1 >= 0, z2 - 2 >= 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 6 + 2*z2 }-> plus(timesIter(0, z1, 1 + s6), timesIter(0, z1, 1 + s7)) :|: s6 >= 0, s6 <= z2 - 2, s7 >= 0, s7 <= 1 + (z2 - 2), z2 - 2 >= 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 7 + 2*z'' }-> plus(timesIter(1 + s10, z1, 0), timesIter(1 + s11, z1, 1 + s12)) :|: s10 >= 0, s10 <= z'' - 2, s11 >= 0, s11 <= z'' - 2, s12 >= 0, s12 <= 0, z2 = 1 + 0, z'' - 2 >= 0, z1 >= 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 6 + 2*z'' + 2*z2 }-> plus(timesIter(1 + s13, z1, 1 + s14), timesIter(1 + s15, z1, 1 + s16)) :|: s13 >= 0, s13 <= z'' - 2, s14 >= 0, s14 <= z2 - 2, s15 >= 0, s15 <= z'' - 2, s16 >= 0, s16 <= 1 + (z2 - 2), z'' - 2 >= 0, z2 - 2 >= 0, z1 >= 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 + 2*z'' }-> plus(timesIter(1 + s8, z1, 0), timesIter(1 + s9, z1, 0)) :|: s8 >= 0, s8 <= z'' - 2, s9 >= 0, s9 <= z'' - 2, z'' - 2 >= 0, z2 = 0, z1 >= 0, z' = 0, z3 >= 0
   p(z') -{ 1 }-> 0 :|: z' = 0
   p(z') -{ 1 }-> z' - 1 :|: z' - 1 >= 0
   plus(z', z'') -{ 1 }-> z'' :|: z'' >= 0, z' = 0
   plus(z', z'') -{ 1 }-> 1 + plus(z' - 1, z'') :|: z' - 1 >= 0, z'' >= 0
   times(z', z'') -{ 1 }-> timesIter(z', z'', 0) :|: z' >= 0, z'' >= 0
   timesIter(z', z'', z1) -{ 3 + z' }-> if(s', 1 + (1 + (1 + (z' - 3))), z'', 0, z'') :|: s' >= 0, s' <= 2, z1 = 0, z' - 3 >= 0, z'' >= 0
   timesIter(z', z'', z1) -{ 3 + z' }-> if(s'', 1 + (1 + (1 + (z' - 3))), z'', 1 + (z1 - 1), 1 + plus(z1 - 1, z'')) :|: s'' >= 0, s'' <= 2, z' - 3 >= 0, z'' >= 0, z1 - 1 >= 0
   timesIter(z', z'', z1) -{ 3 }-> if(2, 0, z'', 0, z'') :|: z1 = 0, z'' >= 0, z' = 0
   timesIter(z', z'', z1) -{ 3 }-> if(2, 0, z'', 1 + (z1 - 1), 1 + plus(z1 - 1, z'')) :|: z'' >= 0, z1 - 1 >= 0, z' = 0
   timesIter(z', z'', z1) -{ 3 }-> if(1, 1 + 0, z'', 0, z'') :|: z1 = 0, z'' >= 0, z' = 1 + 0
   timesIter(z', z'', z1) -{ 3 }-> if(1, 1 + 0, z'', 1 + (z1 - 1), 1 + plus(z1 - 1, z'')) :|: z1 - 1 >= 0, z'' >= 0, z' = 1 + 0
   timesIter(z', z'', z1) -{ 3 }-> if(0, 1 + (1 + 0), z'', 0, z'') :|: z1 = 0, z' = 1 + (1 + 0), z'' >= 0
   timesIter(z', z'', z1) -{ 3 }-> if(0, 1 + (1 + 0), z'', 1 + (z1 - 1), 1 + plus(z1 - 1, z'')) :|: z' = 1 + (1 + 0), z'' >= 0, z1 - 1 >= 0

Function symbols to be analyzed: {plus}, {p}, {timesIter,if}, {times}
Previous analysis results are:
  check: runtime: O(n^1) [2 + z'], size: O(1) [2]
  half: runtime: O(n^1) [2 + z'], size: O(n^1) [z']
  plus: runtime: ?, size: O(n^1) [z' + z'']

----------------------------------------

(35) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: plus
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 1 + z'

----------------------------------------

(36)
Obligation:
Complexity RNTS consisting of the following rules:

   check(z') -{ 1 + z' }-> s :|: s >= 0, s <= 2, z' - 3 >= 0
   check(z') -{ 1 }-> 2 :|: z' = 0
   check(z') -{ 1 }-> 1 :|: z' = 1 + 0
   check(z') -{ 1 }-> 0 :|: z' = 1 + (1 + 0)
   half(z') -{ 1 }-> 0 :|: z' = 0
   half(z') -{ 1 }-> 0 :|: z' = 1 + 0
   half(z') -{ 1 + z' }-> 1 + s1 :|: s1 >= 0, s1 <= z' - 2, z' - 2 >= 0
   if(z', z'', z1, z2, z3) -{ 1 }-> z2 :|: z2 >= 0, z' = 2, z'' >= 0, z1 >= 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 2 }-> timesIter(0, z1, z3) :|: z'' = 0, z2 >= 0, z1 >= 0, z' = 1, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 2 }-> timesIter(z'' - 1, z1, z3) :|: z'' - 1 >= 0, z2 >= 0, z1 >= 0, z' = 1, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 0)) :|: z'' = 0, z2 = 0, z1 >= 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 0)) :|: z2 = 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 7 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 1 + s2)) :|: s2 >= 0, s2 <= 0, z'' = 0, z2 = 1 + 0, z1 >= 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 7 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 1 + s5)) :|: s5 >= 0, s5 <= 0, z2 = 1 + 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 6 + 2*z2 }-> plus(timesIter(0, z1, 1 + s3), timesIter(0, z1, 1 + s4)) :|: s3 >= 0, s3 <= z2 - 2, s4 >= 0, s4 <= 1 + (z2 - 2), z'' = 0, z1 >= 0, z2 - 2 >= 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 6 + 2*z2 }-> plus(timesIter(0, z1, 1 + s6), timesIter(0, z1, 1 + s7)) :|: s6 >= 0, s6 <= z2 - 2, s7 >= 0, s7 <= 1 + (z2 - 2), z2 - 2 >= 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 7 + 2*z'' }-> plus(timesIter(1 + s10, z1, 0), timesIter(1 + s11, z1, 1 + s12)) :|: s10 >= 0, s10 <= z'' - 2, s11 >= 0, s11 <= z'' - 2, s12 >= 0, s12 <= 0, z2 = 1 + 0, z'' - 2 >= 0, z1 >= 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 6 + 2*z'' + 2*z2 }-> plus(timesIter(1 + s13, z1, 1 + s14), timesIter(1 + s15, z1, 1 + s16)) :|: s13 >= 0, s13 <= z'' - 2, s14 >= 0, s14 <= z2 - 2, s15 >= 0, s15 <= z'' - 2, s16 >= 0, s16 <= 1 + (z2 - 2), z'' - 2 >= 0, z2 - 2 >= 0, z1 >= 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 + 2*z'' }-> plus(timesIter(1 + s8, z1, 0), timesIter(1 + s9, z1, 0)) :|: s8 >= 0, s8 <= z'' - 2, s9 >= 0, s9 <= z'' - 2, z'' - 2 >= 0, z2 = 0, z1 >= 0, z' = 0, z3 >= 0
   p(z') -{ 1 }-> 0 :|: z' = 0
   p(z') -{ 1 }-> z' - 1 :|: z' - 1 >= 0
   plus(z', z'') -{ 1 }-> z'' :|: z'' >= 0, z' = 0
   plus(z', z'') -{ 1 }-> 1 + plus(z' - 1, z'') :|: z' - 1 >= 0, z'' >= 0
   times(z', z'') -{ 1 }-> timesIter(z', z'', 0) :|: z' >= 0, z'' >= 0
   timesIter(z', z'', z1) -{ 3 + z' }-> if(s', 1 + (1 + (1 + (z' - 3))), z'', 0, z'') :|: s' >= 0, s' <= 2, z1 = 0, z' - 3 >= 0, z'' >= 0
   timesIter(z', z'', z1) -{ 3 + z' }-> if(s'', 1 + (1 + (1 + (z' - 3))), z'', 1 + (z1 - 1), 1 + plus(z1 - 1, z'')) :|: s'' >= 0, s'' <= 2, z' - 3 >= 0, z'' >= 0, z1 - 1 >= 0
   timesIter(z', z'', z1) -{ 3 }-> if(2, 0, z'', 0, z'') :|: z1 = 0, z'' >= 0, z' = 0
   timesIter(z', z'', z1) -{ 3 }-> if(2, 0, z'', 1 + (z1 - 1), 1 + plus(z1 - 1, z'')) :|: z'' >= 0, z1 - 1 >= 0, z' = 0
   timesIter(z', z'', z1) -{ 3 }-> if(1, 1 + 0, z'', 0, z'') :|: z1 = 0, z'' >= 0, z' = 1 + 0
   timesIter(z', z'', z1) -{ 3 }-> if(1, 1 + 0, z'', 1 + (z1 - 1), 1 + plus(z1 - 1, z'')) :|: z1 - 1 >= 0, z'' >= 0, z' = 1 + 0
   timesIter(z', z'', z1) -{ 3 }-> if(0, 1 + (1 + 0), z'', 0, z'') :|: z1 = 0, z' = 1 + (1 + 0), z'' >= 0
   timesIter(z', z'', z1) -{ 3 }-> if(0, 1 + (1 + 0), z'', 1 + (z1 - 1), 1 + plus(z1 - 1, z'')) :|: z' = 1 + (1 + 0), z'' >= 0, z1 - 1 >= 0

Function symbols to be analyzed: {p}, {timesIter,if}, {times}
Previous analysis results are:
  check: runtime: O(n^1) [2 + z'], size: O(1) [2]
  half: runtime: O(n^1) [2 + z'], size: O(n^1) [z']
  plus: runtime: O(n^1) [1 + z'], size: O(n^1) [z' + z'']

----------------------------------------

(37) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

(38)
Obligation:
Complexity RNTS consisting of the following rules:

   check(z') -{ 1 + z' }-> s :|: s >= 0, s <= 2, z' - 3 >= 0
   check(z') -{ 1 }-> 2 :|: z' = 0
   check(z') -{ 1 }-> 1 :|: z' = 1 + 0
   check(z') -{ 1 }-> 0 :|: z' = 1 + (1 + 0)
   half(z') -{ 1 }-> 0 :|: z' = 0
   half(z') -{ 1 }-> 0 :|: z' = 1 + 0
   half(z') -{ 1 + z' }-> 1 + s1 :|: s1 >= 0, s1 <= z' - 2, z' - 2 >= 0
   if(z', z'', z1, z2, z3) -{ 1 }-> z2 :|: z2 >= 0, z' = 2, z'' >= 0, z1 >= 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 2 }-> timesIter(0, z1, z3) :|: z'' = 0, z2 >= 0, z1 >= 0, z' = 1, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 2 }-> timesIter(z'' - 1, z1, z3) :|: z'' - 1 >= 0, z2 >= 0, z1 >= 0, z' = 1, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 0)) :|: z'' = 0, z2 = 0, z1 >= 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 0)) :|: z2 = 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 7 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 1 + s2)) :|: s2 >= 0, s2 <= 0, z'' = 0, z2 = 1 + 0, z1 >= 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 7 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 1 + s5)) :|: s5 >= 0, s5 <= 0, z2 = 1 + 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 6 + 2*z2 }-> plus(timesIter(0, z1, 1 + s3), timesIter(0, z1, 1 + s4)) :|: s3 >= 0, s3 <= z2 - 2, s4 >= 0, s4 <= 1 + (z2 - 2), z'' = 0, z1 >= 0, z2 - 2 >= 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 6 + 2*z2 }-> plus(timesIter(0, z1, 1 + s6), timesIter(0, z1, 1 + s7)) :|: s6 >= 0, s6 <= z2 - 2, s7 >= 0, s7 <= 1 + (z2 - 2), z2 - 2 >= 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 7 + 2*z'' }-> plus(timesIter(1 + s10, z1, 0), timesIter(1 + s11, z1, 1 + s12)) :|: s10 >= 0, s10 <= z'' - 2, s11 >= 0, s11 <= z'' - 2, s12 >= 0, s12 <= 0, z2 = 1 + 0, z'' - 2 >= 0, z1 >= 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 6 + 2*z'' + 2*z2 }-> plus(timesIter(1 + s13, z1, 1 + s14), timesIter(1 + s15, z1, 1 + s16)) :|: s13 >= 0, s13 <= z'' - 2, s14 >= 0, s14 <= z2 - 2, s15 >= 0, s15 <= z'' - 2, s16 >= 0, s16 <= 1 + (z2 - 2), z'' - 2 >= 0, z2 - 2 >= 0, z1 >= 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 + 2*z'' }-> plus(timesIter(1 + s8, z1, 0), timesIter(1 + s9, z1, 0)) :|: s8 >= 0, s8 <= z'' - 2, s9 >= 0, s9 <= z'' - 2, z'' - 2 >= 0, z2 = 0, z1 >= 0, z' = 0, z3 >= 0
   p(z') -{ 1 }-> 0 :|: z' = 0
   p(z') -{ 1 }-> z' - 1 :|: z' - 1 >= 0
   plus(z', z'') -{ 1 }-> z'' :|: z'' >= 0, z' = 0
   plus(z', z'') -{ 1 + z' }-> 1 + s17 :|: s17 >= 0, s17 <= z' - 1 + z'', z' - 1 >= 0, z'' >= 0
   times(z', z'') -{ 1 }-> timesIter(z', z'', 0) :|: z' >= 0, z'' >= 0
   timesIter(z', z'', z1) -{ 3 + z' }-> if(s', 1 + (1 + (1 + (z' - 3))), z'', 0, z'') :|: s' >= 0, s' <= 2, z1 = 0, z' - 3 >= 0, z'' >= 0
   timesIter(z', z'', z1) -{ 3 + z' + z1 }-> if(s'', 1 + (1 + (1 + (z' - 3))), z'', 1 + (z1 - 1), 1 + s21) :|: s21 >= 0, s21 <= z1 - 1 + z'', s'' >= 0, s'' <= 2, z' - 3 >= 0, z'' >= 0, z1 - 1 >= 0
   timesIter(z', z'', z1) -{ 3 }-> if(2, 0, z'', 0, z'') :|: z1 = 0, z'' >= 0, z' = 0
   timesIter(z', z'', z1) -{ 3 + z1 }-> if(2, 0, z'', 1 + (z1 - 1), 1 + s18) :|: s18 >= 0, s18 <= z1 - 1 + z'', z'' >= 0, z1 - 1 >= 0, z' = 0
   timesIter(z', z'', z1) -{ 3 }-> if(1, 1 + 0, z'', 0, z'') :|: z1 = 0, z'' >= 0, z' = 1 + 0
   timesIter(z', z'', z1) -{ 3 + z1 }-> if(1, 1 + 0, z'', 1 + (z1 - 1), 1 + s19) :|: s19 >= 0, s19 <= z1 - 1 + z'', z1 - 1 >= 0, z'' >= 0, z' = 1 + 0
   timesIter(z', z'', z1) -{ 3 }-> if(0, 1 + (1 + 0), z'', 0, z'') :|: z1 = 0, z' = 1 + (1 + 0), z'' >= 0
   timesIter(z', z'', z1) -{ 3 + z1 }-> if(0, 1 + (1 + 0), z'', 1 + (z1 - 1), 1 + s20) :|: s20 >= 0, s20 <= z1 - 1 + z'', z' = 1 + (1 + 0), z'' >= 0, z1 - 1 >= 0

Function symbols to be analyzed: {p}, {timesIter,if}, {times}
Previous analysis results are:
  check: runtime: O(n^1) [2 + z'], size: O(1) [2]
  half: runtime: O(n^1) [2 + z'], size: O(n^1) [z']
  plus: runtime: O(n^1) [1 + z'], size: O(n^1) [z' + z'']

----------------------------------------

(39) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using KoAT for: p
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: z'

----------------------------------------

(40)
Obligation:
Complexity RNTS consisting of the following rules:

   check(z') -{ 1 + z' }-> s :|: s >= 0, s <= 2, z' - 3 >= 0
   check(z') -{ 1 }-> 2 :|: z' = 0
   check(z') -{ 1 }-> 1 :|: z' = 1 + 0
   check(z') -{ 1 }-> 0 :|: z' = 1 + (1 + 0)
   half(z') -{ 1 }-> 0 :|: z' = 0
   half(z') -{ 1 }-> 0 :|: z' = 1 + 0
   half(z') -{ 1 + z' }-> 1 + s1 :|: s1 >= 0, s1 <= z' - 2, z' - 2 >= 0
   if(z', z'', z1, z2, z3) -{ 1 }-> z2 :|: z2 >= 0, z' = 2, z'' >= 0, z1 >= 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 2 }-> timesIter(0, z1, z3) :|: z'' = 0, z2 >= 0, z1 >= 0, z' = 1, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 2 }-> timesIter(z'' - 1, z1, z3) :|: z'' - 1 >= 0, z2 >= 0, z1 >= 0, z' = 1, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 0)) :|: z'' = 0, z2 = 0, z1 >= 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 0)) :|: z2 = 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 7 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 1 + s2)) :|: s2 >= 0, s2 <= 0, z'' = 0, z2 = 1 + 0, z1 >= 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 7 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 1 + s5)) :|: s5 >= 0, s5 <= 0, z2 = 1 + 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 6 + 2*z2 }-> plus(timesIter(0, z1, 1 + s3), timesIter(0, z1, 1 + s4)) :|: s3 >= 0, s3 <= z2 - 2, s4 >= 0, s4 <= 1 + (z2 - 2), z'' = 0, z1 >= 0, z2 - 2 >= 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 6 + 2*z2 }-> plus(timesIter(0, z1, 1 + s6), timesIter(0, z1, 1 + s7)) :|: s6 >= 0, s6 <= z2 - 2, s7 >= 0, s7 <= 1 + (z2 - 2), z2 - 2 >= 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 7 + 2*z'' }-> plus(timesIter(1 + s10, z1, 0), timesIter(1 + s11, z1, 1 + s12)) :|: s10 >= 0, s10 <= z'' - 2, s11 >= 0, s11 <= z'' - 2, s12 >= 0, s12 <= 0, z2 = 1 + 0, z'' - 2 >= 0, z1 >= 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 6 + 2*z'' + 2*z2 }-> plus(timesIter(1 + s13, z1, 1 + s14), timesIter(1 + s15, z1, 1 + s16)) :|: s13 >= 0, s13 <= z'' - 2, s14 >= 0, s14 <= z2 - 2, s15 >= 0, s15 <= z'' - 2, s16 >= 0, s16 <= 1 + (z2 - 2), z'' - 2 >= 0, z2 - 2 >= 0, z1 >= 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 + 2*z'' }-> plus(timesIter(1 + s8, z1, 0), timesIter(1 + s9, z1, 0)) :|: s8 >= 0, s8 <= z'' - 2, s9 >= 0, s9 <= z'' - 2, z'' - 2 >= 0, z2 = 0, z1 >= 0, z' = 0, z3 >= 0
   p(z') -{ 1 }-> 0 :|: z' = 0
   p(z') -{ 1 }-> z' - 1 :|: z' - 1 >= 0
   plus(z', z'') -{ 1 }-> z'' :|: z'' >= 0, z' = 0
   plus(z', z'') -{ 1 + z' }-> 1 + s17 :|: s17 >= 0, s17 <= z' - 1 + z'', z' - 1 >= 0, z'' >= 0
   times(z', z'') -{ 1 }-> timesIter(z', z'', 0) :|: z' >= 0, z'' >= 0
   timesIter(z', z'', z1) -{ 3 + z' }-> if(s', 1 + (1 + (1 + (z' - 3))), z'', 0, z'') :|: s' >= 0, s' <= 2, z1 = 0, z' - 3 >= 0, z'' >= 0
   timesIter(z', z'', z1) -{ 3 + z' + z1 }-> if(s'', 1 + (1 + (1 + (z' - 3))), z'', 1 + (z1 - 1), 1 + s21) :|: s21 >= 0, s21 <= z1 - 1 + z'', s'' >= 0, s'' <= 2, z' - 3 >= 0, z'' >= 0, z1 - 1 >= 0
   timesIter(z', z'', z1) -{ 3 }-> if(2, 0, z'', 0, z'') :|: z1 = 0, z'' >= 0, z' = 0
   timesIter(z', z'', z1) -{ 3 + z1 }-> if(2, 0, z'', 1 + (z1 - 1), 1 + s18) :|: s18 >= 0, s18 <= z1 - 1 + z'', z'' >= 0, z1 - 1 >= 0, z' = 0
   timesIter(z', z'', z1) -{ 3 }-> if(1, 1 + 0, z'', 0, z'') :|: z1 = 0, z'' >= 0, z' = 1 + 0
   timesIter(z', z'', z1) -{ 3 + z1 }-> if(1, 1 + 0, z'', 1 + (z1 - 1), 1 + s19) :|: s19 >= 0, s19 <= z1 - 1 + z'', z1 - 1 >= 0, z'' >= 0, z' = 1 + 0
   timesIter(z', z'', z1) -{ 3 }-> if(0, 1 + (1 + 0), z'', 0, z'') :|: z1 = 0, z' = 1 + (1 + 0), z'' >= 0
   timesIter(z', z'', z1) -{ 3 + z1 }-> if(0, 1 + (1 + 0), z'', 1 + (z1 - 1), 1 + s20) :|: s20 >= 0, s20 <= z1 - 1 + z'', z' = 1 + (1 + 0), z'' >= 0, z1 - 1 >= 0

Function symbols to be analyzed: {p}, {timesIter,if}, {times}
Previous analysis results are:
  check: runtime: O(n^1) [2 + z'], size: O(1) [2]
  half: runtime: O(n^1) [2 + z'], size: O(n^1) [z']
  plus: runtime: O(n^1) [1 + z'], size: O(n^1) [z' + z'']
  p: runtime: ?, size: O(n^1) [z']

----------------------------------------

(41) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: p
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 1

----------------------------------------

(42)
Obligation:
Complexity RNTS consisting of the following rules:

   check(z') -{ 1 + z' }-> s :|: s >= 0, s <= 2, z' - 3 >= 0
   check(z') -{ 1 }-> 2 :|: z' = 0
   check(z') -{ 1 }-> 1 :|: z' = 1 + 0
   check(z') -{ 1 }-> 0 :|: z' = 1 + (1 + 0)
   half(z') -{ 1 }-> 0 :|: z' = 0
   half(z') -{ 1 }-> 0 :|: z' = 1 + 0
   half(z') -{ 1 + z' }-> 1 + s1 :|: s1 >= 0, s1 <= z' - 2, z' - 2 >= 0
   if(z', z'', z1, z2, z3) -{ 1 }-> z2 :|: z2 >= 0, z' = 2, z'' >= 0, z1 >= 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 2 }-> timesIter(0, z1, z3) :|: z'' = 0, z2 >= 0, z1 >= 0, z' = 1, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 2 }-> timesIter(z'' - 1, z1, z3) :|: z'' - 1 >= 0, z2 >= 0, z1 >= 0, z' = 1, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 0)) :|: z'' = 0, z2 = 0, z1 >= 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 0)) :|: z2 = 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 7 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 1 + s2)) :|: s2 >= 0, s2 <= 0, z'' = 0, z2 = 1 + 0, z1 >= 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 7 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 1 + s5)) :|: s5 >= 0, s5 <= 0, z2 = 1 + 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 6 + 2*z2 }-> plus(timesIter(0, z1, 1 + s3), timesIter(0, z1, 1 + s4)) :|: s3 >= 0, s3 <= z2 - 2, s4 >= 0, s4 <= 1 + (z2 - 2), z'' = 0, z1 >= 0, z2 - 2 >= 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 6 + 2*z2 }-> plus(timesIter(0, z1, 1 + s6), timesIter(0, z1, 1 + s7)) :|: s6 >= 0, s6 <= z2 - 2, s7 >= 0, s7 <= 1 + (z2 - 2), z2 - 2 >= 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 7 + 2*z'' }-> plus(timesIter(1 + s10, z1, 0), timesIter(1 + s11, z1, 1 + s12)) :|: s10 >= 0, s10 <= z'' - 2, s11 >= 0, s11 <= z'' - 2, s12 >= 0, s12 <= 0, z2 = 1 + 0, z'' - 2 >= 0, z1 >= 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 6 + 2*z'' + 2*z2 }-> plus(timesIter(1 + s13, z1, 1 + s14), timesIter(1 + s15, z1, 1 + s16)) :|: s13 >= 0, s13 <= z'' - 2, s14 >= 0, s14 <= z2 - 2, s15 >= 0, s15 <= z'' - 2, s16 >= 0, s16 <= 1 + (z2 - 2), z'' - 2 >= 0, z2 - 2 >= 0, z1 >= 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 + 2*z'' }-> plus(timesIter(1 + s8, z1, 0), timesIter(1 + s9, z1, 0)) :|: s8 >= 0, s8 <= z'' - 2, s9 >= 0, s9 <= z'' - 2, z'' - 2 >= 0, z2 = 0, z1 >= 0, z' = 0, z3 >= 0
   p(z') -{ 1 }-> 0 :|: z' = 0
   p(z') -{ 1 }-> z' - 1 :|: z' - 1 >= 0
   plus(z', z'') -{ 1 }-> z'' :|: z'' >= 0, z' = 0
   plus(z', z'') -{ 1 + z' }-> 1 + s17 :|: s17 >= 0, s17 <= z' - 1 + z'', z' - 1 >= 0, z'' >= 0
   times(z', z'') -{ 1 }-> timesIter(z', z'', 0) :|: z' >= 0, z'' >= 0
   timesIter(z', z'', z1) -{ 3 + z' }-> if(s', 1 + (1 + (1 + (z' - 3))), z'', 0, z'') :|: s' >= 0, s' <= 2, z1 = 0, z' - 3 >= 0, z'' >= 0
   timesIter(z', z'', z1) -{ 3 + z' + z1 }-> if(s'', 1 + (1 + (1 + (z' - 3))), z'', 1 + (z1 - 1), 1 + s21) :|: s21 >= 0, s21 <= z1 - 1 + z'', s'' >= 0, s'' <= 2, z' - 3 >= 0, z'' >= 0, z1 - 1 >= 0
   timesIter(z', z'', z1) -{ 3 }-> if(2, 0, z'', 0, z'') :|: z1 = 0, z'' >= 0, z' = 0
   timesIter(z', z'', z1) -{ 3 + z1 }-> if(2, 0, z'', 1 + (z1 - 1), 1 + s18) :|: s18 >= 0, s18 <= z1 - 1 + z'', z'' >= 0, z1 - 1 >= 0, z' = 0
   timesIter(z', z'', z1) -{ 3 }-> if(1, 1 + 0, z'', 0, z'') :|: z1 = 0, z'' >= 0, z' = 1 + 0
   timesIter(z', z'', z1) -{ 3 + z1 }-> if(1, 1 + 0, z'', 1 + (z1 - 1), 1 + s19) :|: s19 >= 0, s19 <= z1 - 1 + z'', z1 - 1 >= 0, z'' >= 0, z' = 1 + 0
   timesIter(z', z'', z1) -{ 3 }-> if(0, 1 + (1 + 0), z'', 0, z'') :|: z1 = 0, z' = 1 + (1 + 0), z'' >= 0
   timesIter(z', z'', z1) -{ 3 + z1 }-> if(0, 1 + (1 + 0), z'', 1 + (z1 - 1), 1 + s20) :|: s20 >= 0, s20 <= z1 - 1 + z'', z' = 1 + (1 + 0), z'' >= 0, z1 - 1 >= 0

Function symbols to be analyzed: {timesIter,if}, {times}
Previous analysis results are:
  check: runtime: O(n^1) [2 + z'], size: O(1) [2]
  half: runtime: O(n^1) [2 + z'], size: O(n^1) [z']
  plus: runtime: O(n^1) [1 + z'], size: O(n^1) [z' + z'']
  p: runtime: O(1) [1], size: O(n^1) [z']

----------------------------------------

(43) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

(44)
Obligation:
Complexity RNTS consisting of the following rules:

   check(z') -{ 1 + z' }-> s :|: s >= 0, s <= 2, z' - 3 >= 0
   check(z') -{ 1 }-> 2 :|: z' = 0
   check(z') -{ 1 }-> 1 :|: z' = 1 + 0
   check(z') -{ 1 }-> 0 :|: z' = 1 + (1 + 0)
   half(z') -{ 1 }-> 0 :|: z' = 0
   half(z') -{ 1 }-> 0 :|: z' = 1 + 0
   half(z') -{ 1 + z' }-> 1 + s1 :|: s1 >= 0, s1 <= z' - 2, z' - 2 >= 0
   if(z', z'', z1, z2, z3) -{ 1 }-> z2 :|: z2 >= 0, z' = 2, z'' >= 0, z1 >= 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 2 }-> timesIter(0, z1, z3) :|: z'' = 0, z2 >= 0, z1 >= 0, z' = 1, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 2 }-> timesIter(z'' - 1, z1, z3) :|: z'' - 1 >= 0, z2 >= 0, z1 >= 0, z' = 1, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 0)) :|: z'' = 0, z2 = 0, z1 >= 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 0)) :|: z2 = 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 7 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 1 + s2)) :|: s2 >= 0, s2 <= 0, z'' = 0, z2 = 1 + 0, z1 >= 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 7 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 1 + s5)) :|: s5 >= 0, s5 <= 0, z2 = 1 + 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 6 + 2*z2 }-> plus(timesIter(0, z1, 1 + s3), timesIter(0, z1, 1 + s4)) :|: s3 >= 0, s3 <= z2 - 2, s4 >= 0, s4 <= 1 + (z2 - 2), z'' = 0, z1 >= 0, z2 - 2 >= 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 6 + 2*z2 }-> plus(timesIter(0, z1, 1 + s6), timesIter(0, z1, 1 + s7)) :|: s6 >= 0, s6 <= z2 - 2, s7 >= 0, s7 <= 1 + (z2 - 2), z2 - 2 >= 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 7 + 2*z'' }-> plus(timesIter(1 + s10, z1, 0), timesIter(1 + s11, z1, 1 + s12)) :|: s10 >= 0, s10 <= z'' - 2, s11 >= 0, s11 <= z'' - 2, s12 >= 0, s12 <= 0, z2 = 1 + 0, z'' - 2 >= 0, z1 >= 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 6 + 2*z'' + 2*z2 }-> plus(timesIter(1 + s13, z1, 1 + s14), timesIter(1 + s15, z1, 1 + s16)) :|: s13 >= 0, s13 <= z'' - 2, s14 >= 0, s14 <= z2 - 2, s15 >= 0, s15 <= z'' - 2, s16 >= 0, s16 <= 1 + (z2 - 2), z'' - 2 >= 0, z2 - 2 >= 0, z1 >= 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 + 2*z'' }-> plus(timesIter(1 + s8, z1, 0), timesIter(1 + s9, z1, 0)) :|: s8 >= 0, s8 <= z'' - 2, s9 >= 0, s9 <= z'' - 2, z'' - 2 >= 0, z2 = 0, z1 >= 0, z' = 0, z3 >= 0
   p(z') -{ 1 }-> 0 :|: z' = 0
   p(z') -{ 1 }-> z' - 1 :|: z' - 1 >= 0
   plus(z', z'') -{ 1 }-> z'' :|: z'' >= 0, z' = 0
   plus(z', z'') -{ 1 + z' }-> 1 + s17 :|: s17 >= 0, s17 <= z' - 1 + z'', z' - 1 >= 0, z'' >= 0
   times(z', z'') -{ 1 }-> timesIter(z', z'', 0) :|: z' >= 0, z'' >= 0
   timesIter(z', z'', z1) -{ 3 + z' }-> if(s', 1 + (1 + (1 + (z' - 3))), z'', 0, z'') :|: s' >= 0, s' <= 2, z1 = 0, z' - 3 >= 0, z'' >= 0
   timesIter(z', z'', z1) -{ 3 + z' + z1 }-> if(s'', 1 + (1 + (1 + (z' - 3))), z'', 1 + (z1 - 1), 1 + s21) :|: s21 >= 0, s21 <= z1 - 1 + z'', s'' >= 0, s'' <= 2, z' - 3 >= 0, z'' >= 0, z1 - 1 >= 0
   timesIter(z', z'', z1) -{ 3 }-> if(2, 0, z'', 0, z'') :|: z1 = 0, z'' >= 0, z' = 0
   timesIter(z', z'', z1) -{ 3 + z1 }-> if(2, 0, z'', 1 + (z1 - 1), 1 + s18) :|: s18 >= 0, s18 <= z1 - 1 + z'', z'' >= 0, z1 - 1 >= 0, z' = 0
   timesIter(z', z'', z1) -{ 3 }-> if(1, 1 + 0, z'', 0, z'') :|: z1 = 0, z'' >= 0, z' = 1 + 0
   timesIter(z', z'', z1) -{ 3 + z1 }-> if(1, 1 + 0, z'', 1 + (z1 - 1), 1 + s19) :|: s19 >= 0, s19 <= z1 - 1 + z'', z1 - 1 >= 0, z'' >= 0, z' = 1 + 0
   timesIter(z', z'', z1) -{ 3 }-> if(0, 1 + (1 + 0), z'', 0, z'') :|: z1 = 0, z' = 1 + (1 + 0), z'' >= 0
   timesIter(z', z'', z1) -{ 3 + z1 }-> if(0, 1 + (1 + 0), z'', 1 + (z1 - 1), 1 + s20) :|: s20 >= 0, s20 <= z1 - 1 + z'', z' = 1 + (1 + 0), z'' >= 0, z1 - 1 >= 0

Function symbols to be analyzed: {timesIter,if}, {times}
Previous analysis results are:
  check: runtime: O(n^1) [2 + z'], size: O(1) [2]
  half: runtime: O(n^1) [2 + z'], size: O(n^1) [z']
  plus: runtime: O(n^1) [1 + z'], size: O(n^1) [z' + z'']
  p: runtime: O(1) [1], size: O(n^1) [z']

----------------------------------------

(45) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using KoAT for: timesIter
after applying outer abstraction to obtain an ITS,
resulting in: EXP with polynomial bound: ?

Computed SIZE bound using CoFloCo for: if
after applying outer abstraction to obtain an ITS,
resulting in: INF with polynomial bound: ?

----------------------------------------

(46)
Obligation:
Complexity RNTS consisting of the following rules:

   check(z') -{ 1 + z' }-> s :|: s >= 0, s <= 2, z' - 3 >= 0
   check(z') -{ 1 }-> 2 :|: z' = 0
   check(z') -{ 1 }-> 1 :|: z' = 1 + 0
   check(z') -{ 1 }-> 0 :|: z' = 1 + (1 + 0)
   half(z') -{ 1 }-> 0 :|: z' = 0
   half(z') -{ 1 }-> 0 :|: z' = 1 + 0
   half(z') -{ 1 + z' }-> 1 + s1 :|: s1 >= 0, s1 <= z' - 2, z' - 2 >= 0
   if(z', z'', z1, z2, z3) -{ 1 }-> z2 :|: z2 >= 0, z' = 2, z'' >= 0, z1 >= 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 2 }-> timesIter(0, z1, z3) :|: z'' = 0, z2 >= 0, z1 >= 0, z' = 1, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 2 }-> timesIter(z'' - 1, z1, z3) :|: z'' - 1 >= 0, z2 >= 0, z1 >= 0, z' = 1, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 0)) :|: z'' = 0, z2 = 0, z1 >= 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 0)) :|: z2 = 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 7 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 1 + s2)) :|: s2 >= 0, s2 <= 0, z'' = 0, z2 = 1 + 0, z1 >= 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 7 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 1 + s5)) :|: s5 >= 0, s5 <= 0, z2 = 1 + 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 6 + 2*z2 }-> plus(timesIter(0, z1, 1 + s3), timesIter(0, z1, 1 + s4)) :|: s3 >= 0, s3 <= z2 - 2, s4 >= 0, s4 <= 1 + (z2 - 2), z'' = 0, z1 >= 0, z2 - 2 >= 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 6 + 2*z2 }-> plus(timesIter(0, z1, 1 + s6), timesIter(0, z1, 1 + s7)) :|: s6 >= 0, s6 <= z2 - 2, s7 >= 0, s7 <= 1 + (z2 - 2), z2 - 2 >= 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 7 + 2*z'' }-> plus(timesIter(1 + s10, z1, 0), timesIter(1 + s11, z1, 1 + s12)) :|: s10 >= 0, s10 <= z'' - 2, s11 >= 0, s11 <= z'' - 2, s12 >= 0, s12 <= 0, z2 = 1 + 0, z'' - 2 >= 0, z1 >= 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 6 + 2*z'' + 2*z2 }-> plus(timesIter(1 + s13, z1, 1 + s14), timesIter(1 + s15, z1, 1 + s16)) :|: s13 >= 0, s13 <= z'' - 2, s14 >= 0, s14 <= z2 - 2, s15 >= 0, s15 <= z'' - 2, s16 >= 0, s16 <= 1 + (z2 - 2), z'' - 2 >= 0, z2 - 2 >= 0, z1 >= 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 + 2*z'' }-> plus(timesIter(1 + s8, z1, 0), timesIter(1 + s9, z1, 0)) :|: s8 >= 0, s8 <= z'' - 2, s9 >= 0, s9 <= z'' - 2, z'' - 2 >= 0, z2 = 0, z1 >= 0, z' = 0, z3 >= 0
   p(z') -{ 1 }-> 0 :|: z' = 0
   p(z') -{ 1 }-> z' - 1 :|: z' - 1 >= 0
   plus(z', z'') -{ 1 }-> z'' :|: z'' >= 0, z' = 0
   plus(z', z'') -{ 1 + z' }-> 1 + s17 :|: s17 >= 0, s17 <= z' - 1 + z'', z' - 1 >= 0, z'' >= 0
   times(z', z'') -{ 1 }-> timesIter(z', z'', 0) :|: z' >= 0, z'' >= 0
   timesIter(z', z'', z1) -{ 3 + z' }-> if(s', 1 + (1 + (1 + (z' - 3))), z'', 0, z'') :|: s' >= 0, s' <= 2, z1 = 0, z' - 3 >= 0, z'' >= 0
   timesIter(z', z'', z1) -{ 3 + z' + z1 }-> if(s'', 1 + (1 + (1 + (z' - 3))), z'', 1 + (z1 - 1), 1 + s21) :|: s21 >= 0, s21 <= z1 - 1 + z'', s'' >= 0, s'' <= 2, z' - 3 >= 0, z'' >= 0, z1 - 1 >= 0
   timesIter(z', z'', z1) -{ 3 }-> if(2, 0, z'', 0, z'') :|: z1 = 0, z'' >= 0, z' = 0
   timesIter(z', z'', z1) -{ 3 + z1 }-> if(2, 0, z'', 1 + (z1 - 1), 1 + s18) :|: s18 >= 0, s18 <= z1 - 1 + z'', z'' >= 0, z1 - 1 >= 0, z' = 0
   timesIter(z', z'', z1) -{ 3 }-> if(1, 1 + 0, z'', 0, z'') :|: z1 = 0, z'' >= 0, z' = 1 + 0
   timesIter(z', z'', z1) -{ 3 + z1 }-> if(1, 1 + 0, z'', 1 + (z1 - 1), 1 + s19) :|: s19 >= 0, s19 <= z1 - 1 + z'', z1 - 1 >= 0, z'' >= 0, z' = 1 + 0
   timesIter(z', z'', z1) -{ 3 }-> if(0, 1 + (1 + 0), z'', 0, z'') :|: z1 = 0, z' = 1 + (1 + 0), z'' >= 0
   timesIter(z', z'', z1) -{ 3 + z1 }-> if(0, 1 + (1 + 0), z'', 1 + (z1 - 1), 1 + s20) :|: s20 >= 0, s20 <= z1 - 1 + z'', z' = 1 + (1 + 0), z'' >= 0, z1 - 1 >= 0

Function symbols to be analyzed: {timesIter,if}, {times}
Previous analysis results are:
  check: runtime: O(n^1) [2 + z'], size: O(1) [2]
  half: runtime: O(n^1) [2 + z'], size: O(n^1) [z']
  plus: runtime: O(n^1) [1 + z'], size: O(n^1) [z' + z'']
  p: runtime: O(1) [1], size: O(n^1) [z']
  timesIter: runtime: ?, size: EXP
  if: runtime: ?, size: INF

----------------------------------------

(47) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: timesIter
after applying outer abstraction to obtain an ITS,
resulting in: INF with polynomial bound: ?

----------------------------------------

(48)
Obligation:
Complexity RNTS consisting of the following rules:

   check(z') -{ 1 + z' }-> s :|: s >= 0, s <= 2, z' - 3 >= 0
   check(z') -{ 1 }-> 2 :|: z' = 0
   check(z') -{ 1 }-> 1 :|: z' = 1 + 0
   check(z') -{ 1 }-> 0 :|: z' = 1 + (1 + 0)
   half(z') -{ 1 }-> 0 :|: z' = 0
   half(z') -{ 1 }-> 0 :|: z' = 1 + 0
   half(z') -{ 1 + z' }-> 1 + s1 :|: s1 >= 0, s1 <= z' - 2, z' - 2 >= 0
   if(z', z'', z1, z2, z3) -{ 1 }-> z2 :|: z2 >= 0, z' = 2, z'' >= 0, z1 >= 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 2 }-> timesIter(0, z1, z3) :|: z'' = 0, z2 >= 0, z1 >= 0, z' = 1, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 2 }-> timesIter(z'' - 1, z1, z3) :|: z'' - 1 >= 0, z2 >= 0, z1 >= 0, z' = 1, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 0)) :|: z'' = 0, z2 = 0, z1 >= 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 0)) :|: z2 = 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 7 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 1 + s2)) :|: s2 >= 0, s2 <= 0, z'' = 0, z2 = 1 + 0, z1 >= 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 7 }-> plus(timesIter(0, z1, 0), timesIter(0, z1, 1 + s5)) :|: s5 >= 0, s5 <= 0, z2 = 1 + 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 6 + 2*z2 }-> plus(timesIter(0, z1, 1 + s3), timesIter(0, z1, 1 + s4)) :|: s3 >= 0, s3 <= z2 - 2, s4 >= 0, s4 <= 1 + (z2 - 2), z'' = 0, z1 >= 0, z2 - 2 >= 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 6 + 2*z2 }-> plus(timesIter(0, z1, 1 + s6), timesIter(0, z1, 1 + s7)) :|: s6 >= 0, s6 <= z2 - 2, s7 >= 0, s7 <= 1 + (z2 - 2), z2 - 2 >= 0, z1 >= 0, z'' = 1 + 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 7 + 2*z'' }-> plus(timesIter(1 + s10, z1, 0), timesIter(1 + s11, z1, 1 + s12)) :|: s10 >= 0, s10 <= z'' - 2, s11 >= 0, s11 <= z'' - 2, s12 >= 0, s12 <= 0, z2 = 1 + 0, z'' - 2 >= 0, z1 >= 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 6 + 2*z'' + 2*z2 }-> plus(timesIter(1 + s13, z1, 1 + s14), timesIter(1 + s15, z1, 1 + s16)) :|: s13 >= 0, s13 <= z'' - 2, s14 >= 0, s14 <= z2 - 2, s15 >= 0, s15 <= z'' - 2, s16 >= 0, s16 <= 1 + (z2 - 2), z'' - 2 >= 0, z2 - 2 >= 0, z1 >= 0, z' = 0, z3 >= 0
   if(z', z'', z1, z2, z3) -{ 5 + 2*z'' }-> plus(timesIter(1 + s8, z1, 0), timesIter(1 + s9, z1, 0)) :|: s8 >= 0, s8 <= z'' - 2, s9 >= 0, s9 <= z'' - 2, z'' - 2 >= 0, z2 = 0, z1 >= 0, z' = 0, z3 >= 0
   p(z') -{ 1 }-> 0 :|: z' = 0
   p(z') -{ 1 }-> z' - 1 :|: z' - 1 >= 0
   plus(z', z'') -{ 1 }-> z'' :|: z'' >= 0, z' = 0
   plus(z', z'') -{ 1 + z' }-> 1 + s17 :|: s17 >= 0, s17 <= z' - 1 + z'', z' - 1 >= 0, z'' >= 0
   times(z', z'') -{ 1 }-> timesIter(z', z'', 0) :|: z' >= 0, z'' >= 0
   timesIter(z', z'', z1) -{ 3 + z' }-> if(s', 1 + (1 + (1 + (z' - 3))), z'', 0, z'') :|: s' >= 0, s' <= 2, z1 = 0, z' - 3 >= 0, z'' >= 0
   timesIter(z', z'', z1) -{ 3 + z' + z1 }-> if(s'', 1 + (1 + (1 + (z' - 3))), z'', 1 + (z1 - 1), 1 + s21) :|: s21 >= 0, s21 <= z1 - 1 + z'', s'' >= 0, s'' <= 2, z' - 3 >= 0, z'' >= 0, z1 - 1 >= 0
   timesIter(z', z'', z1) -{ 3 }-> if(2, 0, z'', 0, z'') :|: z1 = 0, z'' >= 0, z' = 0
   timesIter(z', z'', z1) -{ 3 + z1 }-> if(2, 0, z'', 1 + (z1 - 1), 1 + s18) :|: s18 >= 0, s18 <= z1 - 1 + z'', z'' >= 0, z1 - 1 >= 0, z' = 0
   timesIter(z', z'', z1) -{ 3 }-> if(1, 1 + 0, z'', 0, z'') :|: z1 = 0, z'' >= 0, z' = 1 + 0
   timesIter(z', z'', z1) -{ 3 + z1 }-> if(1, 1 + 0, z'', 1 + (z1 - 1), 1 + s19) :|: s19 >= 0, s19 <= z1 - 1 + z'', z1 - 1 >= 0, z'' >= 0, z' = 1 + 0
   timesIter(z', z'', z1) -{ 3 }-> if(0, 1 + (1 + 0), z'', 0, z'') :|: z1 = 0, z' = 1 + (1 + 0), z'' >= 0
   timesIter(z', z'', z1) -{ 3 + z1 }-> if(0, 1 + (1 + 0), z'', 1 + (z1 - 1), 1 + s20) :|: s20 >= 0, s20 <= z1 - 1 + z'', z' = 1 + (1 + 0), z'' >= 0, z1 - 1 >= 0

Function symbols to be analyzed: {timesIter,if}, {times}
Previous analysis results are:
  check: runtime: O(n^1) [2 + z'], size: O(1) [2]
  half: runtime: O(n^1) [2 + z'], size: O(n^1) [z']
  plus: runtime: O(n^1) [1 + z'], size: O(n^1) [z' + z'']
  p: runtime: O(1) [1], size: O(n^1) [z']
  timesIter: runtime: INF, size: EXP
  if: runtime: ?, size: INF

----------------------------------------

(49) CompletionProof (UPPER BOUND(ID))
The TRS is a completely defined constructor system, as every type has a constant constructor and the following rules were added:
none

And the following fresh constants: none

----------------------------------------

(50)
Obligation:
Runtime Complexity Weighted TRS where all functions are completely defined. The underlying TRS is:

Runtime Complexity Weighted TRS with Types.
The TRS R consists of the following rules:

   check(0) -> zero [1]
   check(s(0)) -> odd [1]
   check(s(s(0))) -> even [1]
   check(s(s(s(x)))) -> check(s(x)) [1]
   half(0) -> 0 [1]
   half(s(0)) -> 0 [1]
   half(s(s(x))) -> s(half(x)) [1]
   plus(0, y) -> y [1]
   plus(s(x), y) -> s(plus(x, y)) [1]
   times(x, y) -> timesIter(x, y, 0) [1]
   timesIter(x, y, z) -> if(check(x), x, y, z, plus(z, y)) [1]
   p(s(x)) -> x [1]
   p(0) -> 0 [1]
   if(zero, x, y, z, u) -> z [1]
   if(odd, x, y, z, u) -> timesIter(p(x), y, u) [1]
   if(even, x, y, z, u) -> plus(timesIter(half(x), y, half(z)), timesIter(half(x), y, half(s(z)))) [1]

The TRS has the following type information:
check :: 0:s -> zero:odd:even
0 :: 0:s
zero :: zero:odd:even
s :: 0:s -> 0:s
odd :: zero:odd:even
even :: zero:odd:even
half :: 0:s -> 0:s
plus :: 0:s -> 0:s -> 0:s
times :: 0:s -> 0:s -> 0:s
timesIter :: 0:s -> 0:s -> 0:s -> 0:s
if :: zero:odd:even -> 0:s -> 0:s -> 0:s -> 0:s -> 0:s
p :: 0:s -> 0:s

Rewrite Strategy: INNERMOST
----------------------------------------

(51) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID))
Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction.
The constant constructors are abstracted as follows:

   0 => 0
   zero => 2
   odd => 1
   even => 0

----------------------------------------

(52)
Obligation:
Complexity RNTS consisting of the following rules:

   check(z') -{ 1 }-> check(1 + x) :|: x >= 0, z' = 1 + (1 + (1 + x))
   check(z') -{ 1 }-> 2 :|: z' = 0
   check(z') -{ 1 }-> 1 :|: z' = 1 + 0
   check(z') -{ 1 }-> 0 :|: z' = 1 + (1 + 0)
   half(z') -{ 1 }-> 0 :|: z' = 0
   half(z') -{ 1 }-> 0 :|: z' = 1 + 0
   half(z') -{ 1 }-> 1 + half(x) :|: x >= 0, z' = 1 + (1 + x)
   if(z', z'', z1, z2, z3) -{ 1 }-> z :|: z1 = y, z >= 0, z' = 2, z2 = z, x >= 0, y >= 0, z'' = x, z3 = u, u >= 0
   if(z', z'', z1, z2, z3) -{ 1 }-> timesIter(p(x), y, u) :|: z1 = y, z >= 0, z2 = z, x >= 0, y >= 0, z'' = x, z' = 1, z3 = u, u >= 0
   if(z', z'', z1, z2, z3) -{ 1 }-> plus(timesIter(half(x), y, half(z)), timesIter(half(x), y, half(1 + z))) :|: z1 = y, z >= 0, z2 = z, x >= 0, y >= 0, z'' = x, z3 = u, z' = 0, u >= 0
   p(z') -{ 1 }-> x :|: z' = 1 + x, x >= 0
   p(z') -{ 1 }-> 0 :|: z' = 0
   plus(z', z'') -{ 1 }-> y :|: z'' = y, y >= 0, z' = 0
   plus(z', z'') -{ 1 }-> 1 + plus(x, y) :|: z' = 1 + x, z'' = y, x >= 0, y >= 0
   times(z', z'') -{ 1 }-> timesIter(x, y, 0) :|: z' = x, z'' = y, x >= 0, y >= 0
   timesIter(z', z'', z1) -{ 1 }-> if(check(x), x, y, z, plus(z, y)) :|: z1 = z, z >= 0, z' = x, z'' = y, x >= 0, y >= 0

Only complete derivations are relevant for the runtime complexity.

----------------------------------------

(53) CpxTrsToCdtProof (UPPER BOUND(ID))
Converted Cpx (relative) TRS with rewrite strategy PARALLEL_INNERMOST to CDT
----------------------------------------

(54)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   times(z0, z1) -> timesIter(z0, z1, 0)
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   p(s(z0)) -> z0
   p(0) -> 0
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
Tuples:
   CHECK(0) -> c
   CHECK(s(0)) -> c1
   CHECK(s(s(0))) -> c2
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(0) -> c4
   HALF(s(0)) -> c5
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(0, z0) -> c7
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   TIMES(z0, z1) -> c9(TIMESITER(z0, z1, 0))
   TIMESITER(z0, z1, z2) -> c10(IF(check(z0), z0, z1, z2, plus(z2, z1)), CHECK(z0))
   TIMESITER(z0, z1, z2) -> c11(IF(check(z0), z0, z1, z2, plus(z2, z1)), PLUS(z2, z1))
   P(s(z0)) -> c12
   P(0) -> c13
   IF(zero, z0, z1, z2, z3) -> c14
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3), P(z0))
   IF(even, z0, z1, z2, z3) -> c16(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z0))
   IF(even, z0, z1, z2, z3) -> c17(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z2))
   IF(even, z0, z1, z2, z3) -> c18(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(z0))
   IF(even, z0, z1, z2, z3) -> c19(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(s(z2)))
S tuples:
   CHECK(0) -> c
   CHECK(s(0)) -> c1
   CHECK(s(s(0))) -> c2
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(0) -> c4
   HALF(s(0)) -> c5
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(0, z0) -> c7
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   TIMES(z0, z1) -> c9(TIMESITER(z0, z1, 0))
   TIMESITER(z0, z1, z2) -> c10(IF(check(z0), z0, z1, z2, plus(z2, z1)), CHECK(z0))
   TIMESITER(z0, z1, z2) -> c11(IF(check(z0), z0, z1, z2, plus(z2, z1)), PLUS(z2, z1))
   P(s(z0)) -> c12
   P(0) -> c13
   IF(zero, z0, z1, z2, z3) -> c14
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3), P(z0))
   IF(even, z0, z1, z2, z3) -> c16(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z0))
   IF(even, z0, z1, z2, z3) -> c17(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z2))
   IF(even, z0, z1, z2, z3) -> c18(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(z0))
   IF(even, z0, z1, z2, z3) -> c19(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(s(z2)))
K tuples:none
Defined Rule Symbols:   check_1, half_1, plus_2, times_2, timesIter_3, p_1, if_5

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, TIMES_2, TIMESITER_3, P_1, IF_5

Compound Symbols:   c, c1, c2, c3_1, c4, c5, c6_1, c7, c8_1, c9_1, c10_2, c11_2, c12, c13, c14, c15_2, c16_3, c17_3, c18_3, c19_3


----------------------------------------

(55) CdtLeafRemovalProof (ComplexityIfPolyImplication)
Removed 1 leading nodes:
   TIMES(z0, z1) -> c9(TIMESITER(z0, z1, 0))
Removed 9 trailing nodes:
   P(s(z0)) -> c12
   PLUS(0, z0) -> c7
   CHECK(s(s(0))) -> c2
   CHECK(s(0)) -> c1
   IF(zero, z0, z1, z2, z3) -> c14
   CHECK(0) -> c
   HALF(0) -> c4
   P(0) -> c13
   HALF(s(0)) -> c5

----------------------------------------

(56)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   times(z0, z1) -> timesIter(z0, z1, 0)
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   p(s(z0)) -> z0
   p(0) -> 0
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   TIMESITER(z0, z1, z2) -> c10(IF(check(z0), z0, z1, z2, plus(z2, z1)), CHECK(z0))
   TIMESITER(z0, z1, z2) -> c11(IF(check(z0), z0, z1, z2, plus(z2, z1)), PLUS(z2, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3), P(z0))
   IF(even, z0, z1, z2, z3) -> c16(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z0))
   IF(even, z0, z1, z2, z3) -> c17(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z2))
   IF(even, z0, z1, z2, z3) -> c18(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(z0))
   IF(even, z0, z1, z2, z3) -> c19(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(s(z2)))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   TIMESITER(z0, z1, z2) -> c10(IF(check(z0), z0, z1, z2, plus(z2, z1)), CHECK(z0))
   TIMESITER(z0, z1, z2) -> c11(IF(check(z0), z0, z1, z2, plus(z2, z1)), PLUS(z2, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3), P(z0))
   IF(even, z0, z1, z2, z3) -> c16(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z0))
   IF(even, z0, z1, z2, z3) -> c17(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z2))
   IF(even, z0, z1, z2, z3) -> c18(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(z0))
   IF(even, z0, z1, z2, z3) -> c19(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(s(z2)))
K tuples:none
Defined Rule Symbols:   check_1, half_1, plus_2, times_2, timesIter_3, p_1, if_5

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, TIMESITER_3, IF_5

Compound Symbols:   c3_1, c6_1, c8_1, c10_2, c11_2, c15_2, c16_3, c17_3, c18_3, c19_3


----------------------------------------

(57) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing tuple parts
----------------------------------------

(58)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   times(z0, z1) -> timesIter(z0, z1, 0)
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   p(s(z0)) -> z0
   p(0) -> 0
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   TIMESITER(z0, z1, z2) -> c10(IF(check(z0), z0, z1, z2, plus(z2, z1)), CHECK(z0))
   TIMESITER(z0, z1, z2) -> c11(IF(check(z0), z0, z1, z2, plus(z2, z1)), PLUS(z2, z1))
   IF(even, z0, z1, z2, z3) -> c16(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z0))
   IF(even, z0, z1, z2, z3) -> c17(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z2))
   IF(even, z0, z1, z2, z3) -> c18(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(z0))
   IF(even, z0, z1, z2, z3) -> c19(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(s(z2)))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   TIMESITER(z0, z1, z2) -> c10(IF(check(z0), z0, z1, z2, plus(z2, z1)), CHECK(z0))
   TIMESITER(z0, z1, z2) -> c11(IF(check(z0), z0, z1, z2, plus(z2, z1)), PLUS(z2, z1))
   IF(even, z0, z1, z2, z3) -> c16(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z0))
   IF(even, z0, z1, z2, z3) -> c17(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z2))
   IF(even, z0, z1, z2, z3) -> c18(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(z0))
   IF(even, z0, z1, z2, z3) -> c19(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(s(z2)))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
K tuples:none
Defined Rule Symbols:   check_1, half_1, plus_2, times_2, timesIter_3, p_1, if_5

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, TIMESITER_3, IF_5

Compound Symbols:   c3_1, c6_1, c8_1, c10_2, c11_2, c16_3, c17_3, c18_3, c19_3, c15_1


----------------------------------------

(59) CdtUsableRulesProof (BOTH BOUNDS(ID, ID))
The following rules are not usable and were removed:
   times(z0, z1) -> timesIter(z0, z1, 0)

----------------------------------------

(60)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   TIMESITER(z0, z1, z2) -> c10(IF(check(z0), z0, z1, z2, plus(z2, z1)), CHECK(z0))
   TIMESITER(z0, z1, z2) -> c11(IF(check(z0), z0, z1, z2, plus(z2, z1)), PLUS(z2, z1))
   IF(even, z0, z1, z2, z3) -> c16(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z0))
   IF(even, z0, z1, z2, z3) -> c17(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z2))
   IF(even, z0, z1, z2, z3) -> c18(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(z0))
   IF(even, z0, z1, z2, z3) -> c19(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(s(z2)))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   TIMESITER(z0, z1, z2) -> c10(IF(check(z0), z0, z1, z2, plus(z2, z1)), CHECK(z0))
   TIMESITER(z0, z1, z2) -> c11(IF(check(z0), z0, z1, z2, plus(z2, z1)), PLUS(z2, z1))
   IF(even, z0, z1, z2, z3) -> c16(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z0))
   IF(even, z0, z1, z2, z3) -> c17(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z2))
   IF(even, z0, z1, z2, z3) -> c18(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(z0))
   IF(even, z0, z1, z2, z3) -> c19(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(s(z2)))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
K tuples:none
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, TIMESITER_3, IF_5

Compound Symbols:   c3_1, c6_1, c8_1, c10_2, c11_2, c16_3, c17_3, c18_3, c19_3, c15_1


----------------------------------------

(61) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace TIMESITER(z0, z1, z2) -> c10(IF(check(z0), z0, z1, z2, plus(z2, z1)), CHECK(z0)) by 
   TIMESITER(x0, z0, 0) -> c10(IF(check(x0), x0, z0, 0, z0), CHECK(x0))
   TIMESITER(x0, z1, s(z0)) -> c10(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), CHECK(x0))
   TIMESITER(0, x1, x2) -> c10(IF(zero, 0, x1, x2, plus(x2, x1)), CHECK(0))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)), CHECK(s(0)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)), CHECK(s(s(0))))
   TIMESITER(s(s(s(z0))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(z0)))))

----------------------------------------

(62)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   TIMESITER(z0, z1, z2) -> c11(IF(check(z0), z0, z1, z2, plus(z2, z1)), PLUS(z2, z1))
   IF(even, z0, z1, z2, z3) -> c16(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z0))
   IF(even, z0, z1, z2, z3) -> c17(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z2))
   IF(even, z0, z1, z2, z3) -> c18(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(z0))
   IF(even, z0, z1, z2, z3) -> c19(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(s(z2)))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(x0, z0, 0) -> c10(IF(check(x0), x0, z0, 0, z0), CHECK(x0))
   TIMESITER(x0, z1, s(z0)) -> c10(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), CHECK(x0))
   TIMESITER(0, x1, x2) -> c10(IF(zero, 0, x1, x2, plus(x2, x1)), CHECK(0))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)), CHECK(s(0)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)), CHECK(s(s(0))))
   TIMESITER(s(s(s(z0))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(z0)))))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   TIMESITER(z0, z1, z2) -> c11(IF(check(z0), z0, z1, z2, plus(z2, z1)), PLUS(z2, z1))
   IF(even, z0, z1, z2, z3) -> c16(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z0))
   IF(even, z0, z1, z2, z3) -> c17(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z2))
   IF(even, z0, z1, z2, z3) -> c18(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(z0))
   IF(even, z0, z1, z2, z3) -> c19(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(s(z2)))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(x0, z0, 0) -> c10(IF(check(x0), x0, z0, 0, z0), CHECK(x0))
   TIMESITER(x0, z1, s(z0)) -> c10(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), CHECK(x0))
   TIMESITER(0, x1, x2) -> c10(IF(zero, 0, x1, x2, plus(x2, x1)), CHECK(0))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)), CHECK(s(0)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)), CHECK(s(s(0))))
   TIMESITER(s(s(s(z0))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(z0)))))
K tuples:none
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, TIMESITER_3, IF_5

Compound Symbols:   c3_1, c6_1, c8_1, c11_2, c16_3, c17_3, c18_3, c19_3, c15_1, c10_2


----------------------------------------

(63) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   TIMESITER(0, x1, x2) -> c10(IF(zero, 0, x1, x2, plus(x2, x1)), CHECK(0))

----------------------------------------

(64)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   TIMESITER(z0, z1, z2) -> c11(IF(check(z0), z0, z1, z2, plus(z2, z1)), PLUS(z2, z1))
   IF(even, z0, z1, z2, z3) -> c16(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z0))
   IF(even, z0, z1, z2, z3) -> c17(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z2))
   IF(even, z0, z1, z2, z3) -> c18(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(z0))
   IF(even, z0, z1, z2, z3) -> c19(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(s(z2)))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(x0, z0, 0) -> c10(IF(check(x0), x0, z0, 0, z0), CHECK(x0))
   TIMESITER(x0, z1, s(z0)) -> c10(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), CHECK(x0))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)), CHECK(s(0)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)), CHECK(s(s(0))))
   TIMESITER(s(s(s(z0))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(z0)))))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   TIMESITER(z0, z1, z2) -> c11(IF(check(z0), z0, z1, z2, plus(z2, z1)), PLUS(z2, z1))
   IF(even, z0, z1, z2, z3) -> c16(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z0))
   IF(even, z0, z1, z2, z3) -> c17(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z2))
   IF(even, z0, z1, z2, z3) -> c18(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(z0))
   IF(even, z0, z1, z2, z3) -> c19(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(s(z2)))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(x0, z0, 0) -> c10(IF(check(x0), x0, z0, 0, z0), CHECK(x0))
   TIMESITER(x0, z1, s(z0)) -> c10(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), CHECK(x0))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)), CHECK(s(0)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)), CHECK(s(s(0))))
   TIMESITER(s(s(s(z0))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(z0)))))
K tuples:none
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, TIMESITER_3, IF_5

Compound Symbols:   c3_1, c6_1, c8_1, c11_2, c16_3, c17_3, c18_3, c19_3, c15_1, c10_2


----------------------------------------

(65) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing tuple parts
----------------------------------------

(66)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   TIMESITER(z0, z1, z2) -> c11(IF(check(z0), z0, z1, z2, plus(z2, z1)), PLUS(z2, z1))
   IF(even, z0, z1, z2, z3) -> c16(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z0))
   IF(even, z0, z1, z2, z3) -> c17(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z2))
   IF(even, z0, z1, z2, z3) -> c18(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(z0))
   IF(even, z0, z1, z2, z3) -> c19(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(s(z2)))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(x0, z0, 0) -> c10(IF(check(x0), x0, z0, 0, z0), CHECK(x0))
   TIMESITER(x0, z1, s(z0)) -> c10(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   TIMESITER(z0, z1, z2) -> c11(IF(check(z0), z0, z1, z2, plus(z2, z1)), PLUS(z2, z1))
   IF(even, z0, z1, z2, z3) -> c16(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z0))
   IF(even, z0, z1, z2, z3) -> c17(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z2))
   IF(even, z0, z1, z2, z3) -> c18(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(z0))
   IF(even, z0, z1, z2, z3) -> c19(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(s(z2)))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(x0, z0, 0) -> c10(IF(check(x0), x0, z0, 0, z0), CHECK(x0))
   TIMESITER(x0, z1, s(z0)) -> c10(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
K tuples:none
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, TIMESITER_3, IF_5

Compound Symbols:   c3_1, c6_1, c8_1, c11_2, c16_3, c17_3, c18_3, c19_3, c15_1, c10_2, c10_1


----------------------------------------

(67) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace TIMESITER(z0, z1, z2) -> c11(IF(check(z0), z0, z1, z2, plus(z2, z1)), PLUS(z2, z1)) by 
   TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0), PLUS(0, z0))
   TIMESITER(x0, z1, s(z0)) -> c11(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), PLUS(s(z0), z1))
   TIMESITER(0, x1, x2) -> c11(IF(zero, 0, x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))

----------------------------------------

(68)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(even, z0, z1, z2, z3) -> c16(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z0))
   IF(even, z0, z1, z2, z3) -> c17(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z2))
   IF(even, z0, z1, z2, z3) -> c18(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(z0))
   IF(even, z0, z1, z2, z3) -> c19(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(s(z2)))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(x0, z0, 0) -> c10(IF(check(x0), x0, z0, 0, z0), CHECK(x0))
   TIMESITER(x0, z1, s(z0)) -> c10(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0), PLUS(0, z0))
   TIMESITER(x0, z1, s(z0)) -> c11(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), PLUS(s(z0), z1))
   TIMESITER(0, x1, x2) -> c11(IF(zero, 0, x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(even, z0, z1, z2, z3) -> c16(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z0))
   IF(even, z0, z1, z2, z3) -> c17(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z2))
   IF(even, z0, z1, z2, z3) -> c18(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(z0))
   IF(even, z0, z1, z2, z3) -> c19(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(s(z2)))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(x0, z0, 0) -> c10(IF(check(x0), x0, z0, 0, z0), CHECK(x0))
   TIMESITER(x0, z1, s(z0)) -> c10(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0), PLUS(0, z0))
   TIMESITER(x0, z1, s(z0)) -> c11(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), PLUS(s(z0), z1))
   TIMESITER(0, x1, x2) -> c11(IF(zero, 0, x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
K tuples:none
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c16_3, c17_3, c18_3, c19_3, c15_1, c10_2, c10_1, c11_2


----------------------------------------

(69) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing tuple parts
----------------------------------------

(70)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(even, z0, z1, z2, z3) -> c16(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z0))
   IF(even, z0, z1, z2, z3) -> c17(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z2))
   IF(even, z0, z1, z2, z3) -> c18(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(z0))
   IF(even, z0, z1, z2, z3) -> c19(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(s(z2)))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(x0, z0, 0) -> c10(IF(check(x0), x0, z0, 0, z0), CHECK(x0))
   TIMESITER(x0, z1, s(z0)) -> c10(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(x0, z1, s(z0)) -> c11(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), PLUS(s(z0), z1))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(even, z0, z1, z2, z3) -> c16(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z0))
   IF(even, z0, z1, z2, z3) -> c17(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z2))
   IF(even, z0, z1, z2, z3) -> c18(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(z0))
   IF(even, z0, z1, z2, z3) -> c19(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(s(z2)))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(x0, z0, 0) -> c10(IF(check(x0), x0, z0, 0, z0), CHECK(x0))
   TIMESITER(x0, z1, s(z0)) -> c10(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(x0, z1, s(z0)) -> c11(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), PLUS(s(z0), z1))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
K tuples:none
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c16_3, c17_3, c18_3, c19_3, c15_1, c10_2, c10_1, c11_2, c11_1


----------------------------------------

(71) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)))
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
We considered the (Usable) Rules:
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   half(0) -> 0
   p(0) -> 0
   p(s(z0)) -> z0
And the Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(even, z0, z1, z2, z3) -> c16(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z0))
   IF(even, z0, z1, z2, z3) -> c17(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z2))
   IF(even, z0, z1, z2, z3) -> c18(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(z0))
   IF(even, z0, z1, z2, z3) -> c19(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(s(z2)))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(x0, z0, 0) -> c10(IF(check(x0), x0, z0, 0, z0), CHECK(x0))
   TIMESITER(x0, z1, s(z0)) -> c10(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(x0, z1, s(z0)) -> c11(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), PLUS(s(z0), z1))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
The order we found is given by the following interpretation:

Polynomial interpretation :

   POL(0) = [1]
   POL(CHECK(x_1)) = 0
   POL(HALF(x_1)) = 0
   POL(IF(x_1, x_2, x_3, x_4, x_5)) = x_2 + x_3
   POL(PLUS(x_1, x_2)) = 0
   POL(TIMESITER(x_1, x_2, x_3)) = x_1 + x_2
   POL(c10(x_1)) = x_1
   POL(c10(x_1, x_2)) = x_1 + x_2
   POL(c11(x_1)) = x_1
   POL(c11(x_1, x_2)) = x_1 + x_2
   POL(c15(x_1)) = x_1
   POL(c16(x_1, x_2, x_3)) = x_1 + x_2 + x_3
   POL(c17(x_1, x_2, x_3)) = x_1 + x_2 + x_3
   POL(c18(x_1, x_2, x_3)) = x_1 + x_2 + x_3
   POL(c19(x_1, x_2, x_3)) = x_1 + x_2 + x_3
   POL(c3(x_1)) = x_1
   POL(c6(x_1)) = x_1
   POL(c8(x_1)) = x_1
   POL(check(x_1)) = [1]
   POL(even) = [1]
   POL(half(x_1)) = x_1
   POL(if(x_1, x_2, x_3, x_4, x_5)) = [1] + x_1 + x_2 + x_3 + x_4 + x_5
   POL(odd) = [1]
   POL(p(x_1)) = x_1
   POL(plus(x_1, x_2)) = [1]
   POL(s(x_1)) = x_1
   POL(timesIter(x_1, x_2, x_3)) = [1] + x_2
   POL(zero) = [1]

----------------------------------------

(72)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(even, z0, z1, z2, z3) -> c16(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z0))
   IF(even, z0, z1, z2, z3) -> c17(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z2))
   IF(even, z0, z1, z2, z3) -> c18(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(z0))
   IF(even, z0, z1, z2, z3) -> c19(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(s(z2)))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(x0, z0, 0) -> c10(IF(check(x0), x0, z0, 0, z0), CHECK(x0))
   TIMESITER(x0, z1, s(z0)) -> c10(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(x0, z1, s(z0)) -> c11(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), PLUS(s(z0), z1))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(even, z0, z1, z2, z3) -> c16(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z0))
   IF(even, z0, z1, z2, z3) -> c17(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z2))
   IF(even, z0, z1, z2, z3) -> c18(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(z0))
   IF(even, z0, z1, z2, z3) -> c19(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(s(z2)))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(x0, z0, 0) -> c10(IF(check(x0), x0, z0, 0, z0), CHECK(x0))
   TIMESITER(x0, z1, s(z0)) -> c10(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(x0, z1, s(z0)) -> c11(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), PLUS(s(z0), z1))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c16_3, c17_3, c18_3, c19_3, c15_1, c10_2, c10_1, c11_2, c11_1


----------------------------------------

(73) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace IF(even, z0, z1, z2, z3) -> c16(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z0)) by 
   IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(0))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(s(0)))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(0))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(s(0)))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))

----------------------------------------

(74)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(even, z0, z1, z2, z3) -> c17(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z2))
   IF(even, z0, z1, z2, z3) -> c18(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(z0))
   IF(even, z0, z1, z2, z3) -> c19(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(s(z2)))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(x0, z0, 0) -> c10(IF(check(x0), x0, z0, 0, z0), CHECK(x0))
   TIMESITER(x0, z1, s(z0)) -> c10(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(x0, z1, s(z0)) -> c11(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), PLUS(s(z0), z1))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(0))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(s(0)))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(0))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(s(0)))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(even, z0, z1, z2, z3) -> c17(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z2))
   IF(even, z0, z1, z2, z3) -> c18(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(z0))
   IF(even, z0, z1, z2, z3) -> c19(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(s(z2)))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(x0, z0, 0) -> c10(IF(check(x0), x0, z0, 0, z0), CHECK(x0))
   TIMESITER(x0, z1, s(z0)) -> c10(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(x0, z1, s(z0)) -> c11(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), PLUS(s(z0), z1))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(0))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(s(0)))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(0))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(s(0)))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c17_3, c18_3, c19_3, c15_1, c10_2, c10_1, c11_2, c11_1, c16_3


----------------------------------------

(75) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 4 trailing tuple parts
----------------------------------------

(76)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(even, z0, z1, z2, z3) -> c17(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z2))
   IF(even, z0, z1, z2, z3) -> c18(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(z0))
   IF(even, z0, z1, z2, z3) -> c19(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(s(z2)))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(x0, z0, 0) -> c10(IF(check(x0), x0, z0, 0, z0), CHECK(x0))
   TIMESITER(x0, z1, s(z0)) -> c10(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(x0, z1, s(z0)) -> c11(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), PLUS(s(z0), z1))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(even, z0, z1, z2, z3) -> c17(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z2))
   IF(even, z0, z1, z2, z3) -> c18(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(z0))
   IF(even, z0, z1, z2, z3) -> c19(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(s(z2)))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(x0, z0, 0) -> c10(IF(check(x0), x0, z0, 0, z0), CHECK(x0))
   TIMESITER(x0, z1, s(z0)) -> c10(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(x0, z1, s(z0)) -> c11(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), PLUS(s(z0), z1))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c17_3, c18_3, c19_3, c15_1, c10_2, c10_1, c11_2, c11_1, c16_3, c16_2


----------------------------------------

(77) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace IF(even, z0, z1, z2, z3) -> c17(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(z2)), HALF(z2)) by 
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(0))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(0))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(s(0)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))

----------------------------------------

(78)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(even, z0, z1, z2, z3) -> c18(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(z0))
   IF(even, z0, z1, z2, z3) -> c19(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(s(z2)))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(x0, z0, 0) -> c10(IF(check(x0), x0, z0, 0, z0), CHECK(x0))
   TIMESITER(x0, z1, s(z0)) -> c10(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(x0, z1, s(z0)) -> c11(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), PLUS(s(z0), z1))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(0))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(0))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(s(0)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(even, z0, z1, z2, z3) -> c18(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(z0))
   IF(even, z0, z1, z2, z3) -> c19(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(s(z2)))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(x0, z0, 0) -> c10(IF(check(x0), x0, z0, 0, z0), CHECK(x0))
   TIMESITER(x0, z1, s(z0)) -> c10(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(x0, z1, s(z0)) -> c11(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), PLUS(s(z0), z1))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(0))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(0))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(s(0)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c18_3, c19_3, c15_1, c10_2, c10_1, c11_2, c11_1, c16_3, c16_2, c17_3


----------------------------------------

(79) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 3 trailing tuple parts
----------------------------------------

(80)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(even, z0, z1, z2, z3) -> c18(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(z0))
   IF(even, z0, z1, z2, z3) -> c19(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(s(z2)))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(x0, z0, 0) -> c10(IF(check(x0), x0, z0, 0, z0), CHECK(x0))
   TIMESITER(x0, z1, s(z0)) -> c10(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(x0, z1, s(z0)) -> c11(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), PLUS(s(z0), z1))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(even, z0, z1, z2, z3) -> c18(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(z0))
   IF(even, z0, z1, z2, z3) -> c19(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(s(z2)))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(x0, z0, 0) -> c10(IF(check(x0), x0, z0, 0, z0), CHECK(x0))
   TIMESITER(x0, z1, s(z0)) -> c10(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(x0, z1, s(z0)) -> c11(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), PLUS(s(z0), z1))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c18_3, c19_3, c15_1, c10_2, c10_1, c11_2, c11_1, c16_3, c16_2, c17_3, c17_2


----------------------------------------

(81) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace IF(even, z0, z1, z2, z3) -> c18(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(z0)) by 
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(0))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(0)))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(0))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(0)))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))

----------------------------------------

(82)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(even, z0, z1, z2, z3) -> c19(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(s(z2)))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(x0, z0, 0) -> c10(IF(check(x0), x0, z0, 0, z0), CHECK(x0))
   TIMESITER(x0, z1, s(z0)) -> c10(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(x0, z1, s(z0)) -> c11(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), PLUS(s(z0), z1))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(0))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(0)))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(0))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(0)))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(even, z0, z1, z2, z3) -> c19(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(s(z2)))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(x0, z0, 0) -> c10(IF(check(x0), x0, z0, 0, z0), CHECK(x0))
   TIMESITER(x0, z1, s(z0)) -> c10(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(x0, z1, s(z0)) -> c11(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), PLUS(s(z0), z1))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(0))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(0)))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(0))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(0)))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c19_3, c15_1, c10_2, c10_1, c11_2, c11_1, c16_3, c16_2, c17_3, c17_2, c18_3


----------------------------------------

(83) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 4 trailing tuple parts
----------------------------------------

(84)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(even, z0, z1, z2, z3) -> c19(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(s(z2)))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(x0, z0, 0) -> c10(IF(check(x0), x0, z0, 0, z0), CHECK(x0))
   TIMESITER(x0, z1, s(z0)) -> c10(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(x0, z1, s(z0)) -> c11(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), PLUS(s(z0), z1))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(even, z0, z1, z2, z3) -> c19(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(s(z2)))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(x0, z0, 0) -> c10(IF(check(x0), x0, z0, 0, z0), CHECK(x0))
   TIMESITER(x0, z1, s(z0)) -> c10(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(x0, z1, s(z0)) -> c11(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), PLUS(s(z0), z1))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c19_3, c15_1, c10_2, c10_1, c11_2, c11_1, c16_3, c16_2, c17_3, c17_2, c18_3, c18_2


----------------------------------------

(85) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace IF(even, z0, z1, z2, z3) -> c19(PLUS(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2)))), TIMESITER(half(z0), z1, half(s(z2))), HALF(s(z2))) by 
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(s(0)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(s(0)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))

----------------------------------------

(86)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(x0, z0, 0) -> c10(IF(check(x0), x0, z0, 0, z0), CHECK(x0))
   TIMESITER(x0, z1, s(z0)) -> c10(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(x0, z1, s(z0)) -> c11(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), PLUS(s(z0), z1))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(s(0)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(s(0)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(x0, z0, 0) -> c10(IF(check(x0), x0, z0, 0, z0), CHECK(x0))
   TIMESITER(x0, z1, s(z0)) -> c10(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(x0, z1, s(z0)) -> c11(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), PLUS(s(z0), z1))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(s(0)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(s(0)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_2, c10_1, c11_2, c11_1, c16_3, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3


----------------------------------------

(87) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing tuple parts
----------------------------------------

(88)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(x0, z0, 0) -> c10(IF(check(x0), x0, z0, 0, z0), CHECK(x0))
   TIMESITER(x0, z1, s(z0)) -> c10(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(x0, z1, s(z0)) -> c11(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), PLUS(s(z0), z1))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(x0, z0, 0) -> c10(IF(check(x0), x0, z0, 0, z0), CHECK(x0))
   TIMESITER(x0, z1, s(z0)) -> c10(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(x0, z1, s(z0)) -> c11(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), PLUS(s(z0), z1))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_2, c10_1, c11_2, c11_1, c16_3, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2


----------------------------------------

(89) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace TIMESITER(x0, z0, 0) -> c10(IF(check(x0), x0, z0, 0, z0), CHECK(x0)) by 
   TIMESITER(0, x1, 0) -> c10(IF(zero, 0, x1, 0, x1), CHECK(0))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1), CHECK(s(0)))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1), CHECK(s(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))

----------------------------------------

(90)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(x0, z1, s(z0)) -> c10(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(x0, z1, s(z0)) -> c11(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), PLUS(s(z0), z1))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(0, x1, 0) -> c10(IF(zero, 0, x1, 0, x1), CHECK(0))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1), CHECK(s(0)))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1), CHECK(s(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(x0, z1, s(z0)) -> c10(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(x0, z1, s(z0)) -> c11(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), PLUS(s(z0), z1))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(0, x1, 0) -> c10(IF(zero, 0, x1, 0, x1), CHECK(0))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1), CHECK(s(0)))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1), CHECK(s(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_2, c10_1, c11_2, c11_1, c16_3, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2


----------------------------------------

(91) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   TIMESITER(0, x1, 0) -> c10(IF(zero, 0, x1, 0, x1), CHECK(0))

----------------------------------------

(92)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(x0, z1, s(z0)) -> c10(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(x0, z1, s(z0)) -> c11(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), PLUS(s(z0), z1))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1), CHECK(s(0)))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1), CHECK(s(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(x0, z1, s(z0)) -> c10(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(x0, z1, s(z0)) -> c11(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), PLUS(s(z0), z1))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1), CHECK(s(0)))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1), CHECK(s(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_2, c10_1, c11_2, c11_1, c16_3, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2


----------------------------------------

(93) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing tuple parts
----------------------------------------

(94)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(x0, z1, s(z0)) -> c10(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(x0, z1, s(z0)) -> c11(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), PLUS(s(z0), z1))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(x0, z1, s(z0)) -> c10(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(x0, z1, s(z0)) -> c11(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), PLUS(s(z0), z1))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_2, c10_1, c11_2, c11_1, c16_3, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2


----------------------------------------

(95) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace TIMESITER(x0, z1, s(z0)) -> c10(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), CHECK(x0)) by 
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(0, x1, s(x2)) -> c10(IF(zero, 0, x1, s(x2), s(plus(x2, x1))), CHECK(0))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), CHECK(s(0)))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(0))))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))

----------------------------------------

(96)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(s(s(z0))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(x0, z1, s(z0)) -> c11(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), PLUS(s(z0), z1))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(0, x1, s(x2)) -> c10(IF(zero, 0, x1, s(x2), s(plus(x2, x1))), CHECK(0))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), CHECK(s(0)))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(0))))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(s(s(z0))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(x0, z1, s(z0)) -> c11(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), PLUS(s(z0), z1))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(0, x1, s(x2)) -> c10(IF(zero, 0, x1, s(x2), s(plus(x2, x1))), CHECK(0))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), CHECK(s(0)))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(0))))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_2, c10_1, c11_2, c11_1, c16_3, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2


----------------------------------------

(97) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   TIMESITER(0, x1, s(x2)) -> c10(IF(zero, 0, x1, s(x2), s(plus(x2, x1))), CHECK(0))

----------------------------------------

(98)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(s(s(z0))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(x0, z1, s(z0)) -> c11(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), PLUS(s(z0), z1))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), CHECK(s(0)))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(0))))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(s(s(z0))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(x0, z1, s(z0)) -> c11(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), PLUS(s(z0), z1))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), CHECK(s(0)))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(0))))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_2, c10_1, c11_2, c11_1, c16_3, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2


----------------------------------------

(99) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing tuple parts
----------------------------------------

(100)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(s(s(z0))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(x0, z1, s(z0)) -> c11(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), PLUS(s(z0), z1))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(s(s(z0))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(x0, z1, s(z0)) -> c11(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), PLUS(s(z0), z1))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_2, c10_1, c11_2, c11_1, c16_3, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2


----------------------------------------

(101) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace TIMESITER(s(s(s(z0))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(z0))))) by 
   TIMESITER(s(s(s(x0))), z0, 0) -> c10(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0), CHECK(s(s(s(x0)))))
   TIMESITER(s(s(s(x0))), z1, s(z0)) -> c10(IF(check(s(x0)), s(s(s(x0))), z1, s(z0), s(plus(z0, z1))), CHECK(s(s(s(x0)))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))

----------------------------------------

(102)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(x0, z1, s(z0)) -> c11(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), PLUS(s(z0), z1))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(x0, z1, s(z0)) -> c11(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), PLUS(s(z0), z1))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c16_3, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2


----------------------------------------

(103) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)))
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
We considered the (Usable) Rules:none
And the Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(x0, z1, s(z0)) -> c11(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), PLUS(s(z0), z1))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
The order we found is given by the following interpretation:

Polynomial interpretation :

   POL(0) = 0
   POL(CHECK(x_1)) = 0
   POL(HALF(x_1)) = 0
   POL(IF(x_1, x_2, x_3, x_4, x_5)) = [1]
   POL(PLUS(x_1, x_2)) = 0
   POL(TIMESITER(x_1, x_2, x_3)) = [1]
   POL(c10(x_1)) = x_1
   POL(c10(x_1, x_2)) = x_1 + x_2
   POL(c11(x_1)) = x_1
   POL(c11(x_1, x_2)) = x_1 + x_2
   POL(c15(x_1)) = x_1
   POL(c16(x_1, x_2)) = x_1 + x_2
   POL(c16(x_1, x_2, x_3)) = x_1 + x_2 + x_3
   POL(c17(x_1, x_2)) = x_1 + x_2
   POL(c17(x_1, x_2, x_3)) = x_1 + x_2 + x_3
   POL(c18(x_1, x_2)) = x_1 + x_2
   POL(c18(x_1, x_2, x_3)) = x_1 + x_2 + x_3
   POL(c19(x_1, x_2)) = x_1 + x_2
   POL(c19(x_1, x_2, x_3)) = x_1 + x_2 + x_3
   POL(c3(x_1)) = x_1
   POL(c6(x_1)) = x_1
   POL(c8(x_1)) = x_1
   POL(check(x_1)) = 0
   POL(even) = [1]
   POL(half(x_1)) = 0
   POL(if(x_1, x_2, x_3, x_4, x_5)) = [1] + x_3
   POL(odd) = [1]
   POL(p(x_1)) = [1] + x_1
   POL(plus(x_1, x_2)) = 0
   POL(s(x_1)) = 0
   POL(timesIter(x_1, x_2, x_3)) = x_2
   POL(zero) = [1]

----------------------------------------

(104)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(x0, z1, s(z0)) -> c11(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), PLUS(s(z0), z1))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(x0, z1, s(z0)) -> c11(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), PLUS(s(z0), z1))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c16_3, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2


----------------------------------------

(105) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace TIMESITER(x0, z1, s(z0)) -> c11(IF(check(x0), x0, z1, s(z0), s(plus(z0, z1))), PLUS(s(z0), z1)) by 
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(0, x1, s(x2)) -> c11(IF(zero, 0, x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))

----------------------------------------

(106)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(0, x1, s(x2)) -> c11(IF(zero, 0, x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(0, x1, s(x2)) -> c11(IF(zero, 0, x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c16_3, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2


----------------------------------------

(107) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing tuple parts
----------------------------------------

(108)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c16_3, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2


----------------------------------------

(109) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)))
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
We considered the (Usable) Rules:none
And the Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
The order we found is given by the following interpretation:

Polynomial interpretation :

   POL(0) = 0
   POL(CHECK(x_1)) = 0
   POL(HALF(x_1)) = 0
   POL(IF(x_1, x_2, x_3, x_4, x_5)) = [1]
   POL(PLUS(x_1, x_2)) = 0
   POL(TIMESITER(x_1, x_2, x_3)) = [1]
   POL(c10(x_1)) = x_1
   POL(c10(x_1, x_2)) = x_1 + x_2
   POL(c11(x_1)) = x_1
   POL(c11(x_1, x_2)) = x_1 + x_2
   POL(c15(x_1)) = x_1
   POL(c16(x_1, x_2)) = x_1 + x_2
   POL(c16(x_1, x_2, x_3)) = x_1 + x_2 + x_3
   POL(c17(x_1, x_2)) = x_1 + x_2
   POL(c17(x_1, x_2, x_3)) = x_1 + x_2 + x_3
   POL(c18(x_1, x_2)) = x_1 + x_2
   POL(c18(x_1, x_2, x_3)) = x_1 + x_2 + x_3
   POL(c19(x_1, x_2)) = x_1 + x_2
   POL(c19(x_1, x_2, x_3)) = x_1 + x_2 + x_3
   POL(c3(x_1)) = x_1
   POL(c6(x_1)) = x_1
   POL(c8(x_1)) = x_1
   POL(check(x_1)) = 0
   POL(even) = [1]
   POL(half(x_1)) = 0
   POL(if(x_1, x_2, x_3, x_4, x_5)) = [1] + x_3
   POL(odd) = [1]
   POL(p(x_1)) = [1] + x_1
   POL(plus(x_1, x_2)) = 0
   POL(s(x_1)) = 0
   POL(timesIter(x_1, x_2, x_3)) = x_2
   POL(zero) = [1]

----------------------------------------

(110)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c16_3, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2


----------------------------------------

(111) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace TIMESITER(s(s(s(z0))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, x2, plus(x2, x1)), PLUS(x2, x1)) by 
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0), PLUS(0, z0))
   TIMESITER(s(s(s(x0))), z1, s(z0)) -> c11(IF(check(s(x0)), s(s(s(x0))), z1, s(z0), s(plus(z0, z1))), PLUS(s(z0), z1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))

----------------------------------------

(112)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0), PLUS(0, z0))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0), PLUS(0, z0))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c16_3, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2


----------------------------------------

(113) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing tuple parts
----------------------------------------

(114)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c16_3, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2


----------------------------------------

(115) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace TIMESITER(x0, z0, 0) -> c11(IF(check(x0), x0, z0, 0, z0)) by 
   TIMESITER(0, x1, 0) -> c11(IF(zero, 0, x1, 0, x1))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(s(s(s(z0))), x1, 0) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1))

----------------------------------------

(116)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(0, x1, 0) -> c11(IF(zero, 0, x1, 0, x1))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(0, x1, 0) -> c11(IF(zero, 0, x1, 0, x1))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c16_3, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2


----------------------------------------

(117) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   TIMESITER(0, x1, 0) -> c11(IF(zero, 0, x1, 0, x1))

----------------------------------------

(118)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c16_3, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2


----------------------------------------

(119) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace IF(even, x0, z1, x2, x3) -> c16(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) by 
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(0))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(s(0)))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(0))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(s(0)))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(0))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(s(0)))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))

----------------------------------------

(120)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(0))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(s(0)))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(0))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(s(0)))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(0))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(s(0)))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(0))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(s(0)))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(0))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(s(0)))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(0))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(s(0)))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c16_3, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2


----------------------------------------

(121) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 6 trailing tuple parts
----------------------------------------

(122)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c16_3, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2


----------------------------------------

(123) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0)) by 
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, 0, x1, 0, x2) -> c16(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)), TIMESITER(half(0), x1, half(0)), HALF(0))
   IF(even, s(0), x1, 0, x2) -> c16(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)), TIMESITER(half(s(0)), x1, half(0)), HALF(s(0)))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, 0, x1, 0, x2) -> c16(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)), TIMESITER(half(0), x1, half(0)), HALF(0))
   IF(even, s(0), x1, 0, x2) -> c16(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)), TIMESITER(half(s(0)), x1, half(0)), HALF(s(0)))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))

----------------------------------------

(124)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, 0, x1, 0, x2) -> c16(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)), TIMESITER(half(0), x1, half(0)), HALF(0))
   IF(even, s(0), x1, 0, x2) -> c16(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)), TIMESITER(half(s(0)), x1, half(0)), HALF(s(0)))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, 0, x1, 0, x2) -> c16(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)), TIMESITER(half(0), x1, half(0)), HALF(0))
   IF(even, s(0), x1, 0, x2) -> c16(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)), TIMESITER(half(s(0)), x1, half(0)), HALF(s(0)))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, 0, x1, 0, x2) -> c16(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)), TIMESITER(half(0), x1, half(0)), HALF(0))
   IF(even, s(0), x1, 0, x2) -> c16(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)), TIMESITER(half(s(0)), x1, half(0)), HALF(s(0)))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, 0, x1, 0, x2) -> c16(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)), TIMESITER(half(0), x1, half(0)), HALF(0))
   IF(even, s(0), x1, 0, x2) -> c16(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)), TIMESITER(half(s(0)), x1, half(0)), HALF(s(0)))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c16_3, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2


----------------------------------------

(125) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 4 trailing tuple parts
----------------------------------------

(126)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c16(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)), TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c16(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)), TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c16(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)), TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c16(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)), TIMESITER(half(s(0)), x1, half(0)))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c16(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)), TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c16(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)), TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c16(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)), TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c16(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)), TIMESITER(half(s(0)), x1, half(0)))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c16_3, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2


----------------------------------------

(127) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID))
Split RHS of tuples not part of any SCC
----------------------------------------

(128)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c16_3, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c_1


----------------------------------------

(129) CdtKnowledgeProof (BOTH BOUNDS(ID, ID))
The following tuples could be moved from S to K by knowledge propagation:
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))

----------------------------------------

(130)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c16_3, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c_1


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(131) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0)) by 
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(0))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(0)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(0))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(0)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))

----------------------------------------

(132)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(0))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(0)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(0))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(0)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(0))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(0)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(0))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(0)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c16_3, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c_1


----------------------------------------

(133) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 4 trailing tuple parts
----------------------------------------

(134)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c16_3, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c_1


----------------------------------------

(135) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) by 
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(z0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, half(s(z0))), timesIter(s(half(x0)), x1, s(half(z0)))), TIMESITER(half(s(s(x0))), x1, half(s(z0))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))

----------------------------------------

(136)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c16_3, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c_1


----------------------------------------

(137) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x0)) by 
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(z0)), plus(half(s(z0)), x1)), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(0))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(s(0)))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(0))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(s(0)))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(0))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(s(0)))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))

----------------------------------------

(138)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(0))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(s(0)))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(0))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(s(0)))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(0))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(s(0)))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(0))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(s(0)))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(0))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(s(0)))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(0))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(s(0)))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c16_3, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c_1


----------------------------------------

(139) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 6 trailing tuple parts
----------------------------------------

(140)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c16_3, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c_1


----------------------------------------

(141) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0)) by 
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, 0), if(check(half(x0)), half(x0), z1, half(s(0)), plus(half(s(0)), z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, 0, x1, 0, x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))), TIMESITER(half(0), x1, half(0)), HALF(0))
   IF(even, s(0), x1, 0, x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))), TIMESITER(half(s(0)), x1, half(0)), HALF(s(0)))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, 0), timesIter(s(half(z0)), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, 0, x1, 0, x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))), TIMESITER(half(0), x1, half(0)), HALF(0))
   IF(even, s(0), x1, 0, x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))), TIMESITER(half(s(0)), x1, half(0)), HALF(s(0)))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))

----------------------------------------

(142)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, 0, x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))), TIMESITER(half(0), x1, half(0)), HALF(0))
   IF(even, s(0), x1, 0, x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))), TIMESITER(half(s(0)), x1, half(0)), HALF(s(0)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, 0, x1, 0, x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))), TIMESITER(half(0), x1, half(0)), HALF(0))
   IF(even, s(0), x1, 0, x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))), TIMESITER(half(s(0)), x1, half(0)), HALF(s(0)))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, 0, x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))), TIMESITER(half(0), x1, half(0)), HALF(0))
   IF(even, s(0), x1, 0, x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))), TIMESITER(half(s(0)), x1, half(0)), HALF(s(0)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, 0, x1, 0, x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))), TIMESITER(half(0), x1, half(0)), HALF(0))
   IF(even, s(0), x1, 0, x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))), TIMESITER(half(s(0)), x1, half(0)), HALF(s(0)))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c16_3, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c_1


----------------------------------------

(143) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 4 trailing tuple parts
----------------------------------------

(144)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))), TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))), TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))), TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))), TIMESITER(half(s(0)), x1, half(0)))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))), TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))), TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))), TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))), TIMESITER(half(s(0)), x1, half(0)))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c16_3, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c_1


----------------------------------------

(145) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID))
Split RHS of tuples not part of any SCC
----------------------------------------

(146)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c16_3, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c_1, c1_1


----------------------------------------

(147) CdtKnowledgeProof (BOTH BOUNDS(ID, ID))
The following tuples could be moved from S to K by knowledge propagation:
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))

----------------------------------------

(148)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c16_3, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c_1, c1_1


----------------------------------------

(149) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) by 
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(timesIter(half(x0), z1, 0), if(check(half(x0)), half(x0), z1, half(s(s(0))), plus(half(s(s(0))), z1))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))), HALF(0))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))), HALF(s(0)))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, 0), timesIter(s(half(z0)), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))), HALF(0))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))), HALF(s(0)))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))

----------------------------------------

(150)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))), HALF(0))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))), HALF(s(0)))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))), HALF(0))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))), HALF(s(0)))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))), HALF(0))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))), HALF(s(0)))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))), HALF(0))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))), HALF(s(0)))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c16_3, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c_1, c1_1, c16_1


----------------------------------------

(151) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 4 trailing tuple parts
----------------------------------------

(152)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c16_3, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c_1, c1_1, c16_1


----------------------------------------

(153) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) by 
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(x0), z1, s(half(x2))), if(check(half(x0)), half(x0), z1, half(s(s(s(x2)))), plus(half(s(s(s(x2)))), z1))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(x2))), timesIter(half(x0), x1, s(half(s(x2))))), TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(x0))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(0))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(0)))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, s(half(x2))), timesIter(s(half(z0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(0))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(0)))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))

----------------------------------------

(154)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(0))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(0)))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(0))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(0)))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(0))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(0)))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(0))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(0)))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c16_3, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c_1, c1_1, c16_1


----------------------------------------

(155) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 4 trailing tuple parts
----------------------------------------

(156)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c16_3, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c_1, c1_1, c16_1


----------------------------------------

(157) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0)))) by 
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(s(half(x0)), z1, half(x2)), if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(z0), x3) -> c16(PLUS(timesIter(s(half(x0)), x1, half(s(z0))), timesIter(half(s(s(x0))), x1, s(half(z0)))), TIMESITER(half(s(s(x0))), x1, half(s(z0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(s(half(x0)), x1, s(half(z0))), timesIter(half(s(s(x0))), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))

----------------------------------------

(158)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c_1, c1_1, c16_1


----------------------------------------

(159) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) by 
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, 0, x2) -> c16(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)), TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, s(z0), x2) -> c16(PLUS(timesIter(half(0), x0, half(s(z0))), timesIter(0, x0, s(half(z0)))), TIMESITER(half(0), x0, half(s(z0))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, 0, x2) -> c16(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))), TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, s(0), x2) -> c16(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, 0, x0, s(s(z0)), x2) -> c16(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))

----------------------------------------

(160)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, 0, x2) -> c16(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)), TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c16(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))), TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, 0, x2) -> c16(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)), TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c16(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))), TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c_1, c1_1, c16_1


----------------------------------------

(161) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID))
Split RHS of tuples not part of any SCC
----------------------------------------

(162)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c_1, c1_1, c16_1, c2_1


----------------------------------------

(163) CdtKnowledgeProof (BOTH BOUNDS(ID, ID))
The following tuples could be moved from S to K by knowledge propagation:
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))

----------------------------------------

(164)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c_1, c1_1, c16_1, c2_1


----------------------------------------

(165) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) by 
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c16(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)), TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, s(z0), x2) -> c16(PLUS(timesIter(half(s(0)), x0, half(s(z0))), timesIter(0, x0, s(half(z0)))), TIMESITER(half(s(0)), x0, half(s(z0))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(0), x0, 0, x2) -> c16(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))), TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, s(s(z0)), x2) -> c16(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))

----------------------------------------

(166)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c16(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)), TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c16(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))), TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c16(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)), TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c16(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))), TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c_1, c1_1, c16_1, c2_1


----------------------------------------

(167) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID))
Split RHS of tuples not part of any SCC
----------------------------------------

(168)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c_1, c1_1, c16_1, c2_1, c4_1


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(169) CdtKnowledgeProof (BOTH BOUNDS(ID, ID))
The following tuples could be moved from S to K by knowledge propagation:
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))

----------------------------------------

(170)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c_1, c1_1, c16_1, c2_1, c4_1


----------------------------------------

(171) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2))) by 
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(0, z1, half(x1)), if(check(half(0)), half(0), z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, 0, x2) -> c16(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)), TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, s(z0), x2) -> c16(PLUS(timesIter(0, x0, half(s(z0))), timesIter(half(0), x0, s(half(z0)))), TIMESITER(half(0), x0, half(s(z0))))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, 0, x2) -> c16(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))), TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, s(0), x2) -> c16(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, 0, x0, s(s(z0)), x2) -> c16(PLUS(timesIter(0, x0, s(half(z0))), timesIter(half(0), x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))))

----------------------------------------

(172)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c16(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)), TIMESITER(half(0), x0, half(0)))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, 0, x2) -> c16(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))), TIMESITER(half(0), x0, half(0)))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, 0, x0, 0, x2) -> c16(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)), TIMESITER(half(0), x0, half(0)))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, 0, x2) -> c16(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))), TIMESITER(half(0), x0, half(0)))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c_1, c1_1, c16_1, c2_1, c4_1


----------------------------------------

(173) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID))
Split RHS of tuples not part of any SCC
----------------------------------------

(174)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c_1, c1_1, c16_1, c2_1, c4_1, c5_1


----------------------------------------

(175) CdtKnowledgeProof (BOTH BOUNDS(ID, ID))
The following tuples could be moved from S to K by knowledge propagation:
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))

----------------------------------------

(176)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c16_2, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c_1, c1_1, c16_1, c2_1, c4_1, c5_1


----------------------------------------

(177) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2))) by 
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(0, z1, half(x1)), if(check(half(s(0))), half(s(0)), z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c16(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)), TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, s(z0), x2) -> c16(PLUS(timesIter(0, x0, half(s(z0))), timesIter(half(s(0)), x0, s(half(z0)))), TIMESITER(half(s(0)), x0, half(s(z0))))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c16(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))), TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, s(0), x2) -> c16(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(0), x0, s(s(z0)), x2) -> c16(PLUS(timesIter(0, x0, s(half(z0))), timesIter(half(s(0)), x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))))

----------------------------------------

(178)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c16(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)), TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c16(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))), TIMESITER(half(s(0)), x0, half(0)))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c16(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)), TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c16(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))), TIMESITER(half(s(0)), x0, half(0)))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1


----------------------------------------

(179) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID))
Split RHS of tuples not part of any SCC
----------------------------------------

(180)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1


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(181) CdtKnowledgeProof (BOTH BOUNDS(ID, ID))
The following tuples could be moved from S to K by knowledge propagation:
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))

----------------------------------------

(182)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1


----------------------------------------

(183) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace IF(even, x0, z1, x2, x3) -> c17(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) by 
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(0))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(0))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(0))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(s(0)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))

----------------------------------------

(184)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(0))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(0))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(0))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(s(0)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(0))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(0))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(0))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(s(0)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1


----------------------------------------

(185) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 4 trailing tuple parts
----------------------------------------

(186)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1


----------------------------------------

(187) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0))) by 
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(s(0)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(s(0)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))

----------------------------------------

(188)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(s(0)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(s(0)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(s(0)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(s(0)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1


----------------------------------------

(189) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing tuple parts
----------------------------------------

(190)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1


----------------------------------------

(191) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) by 
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, 0, x2) -> c17(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)), TIMESITER(half(0), x0, half(0)), HALF(0))
   IF(even, 0, x0, s(z0), x2) -> c17(PLUS(timesIter(half(0), x0, half(s(z0))), timesIter(0, x0, s(half(z0)))), TIMESITER(half(0), x0, half(s(z0))), HALF(s(z0)))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, 0, x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))), TIMESITER(half(0), x0, half(0)), HALF(0))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))), HALF(s(0)))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))

----------------------------------------

(192)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, 0, x2) -> c17(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)), TIMESITER(half(0), x0, half(0)), HALF(0))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, 0, x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))), TIMESITER(half(0), x0, half(0)), HALF(0))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))), HALF(s(0)))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, 0, x2) -> c17(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)), TIMESITER(half(0), x0, half(0)), HALF(0))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, 0, x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))), TIMESITER(half(0), x0, half(0)), HALF(0))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))), HALF(s(0)))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1


----------------------------------------

(193) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 3 trailing tuple parts
----------------------------------------

(194)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
   IF(even, 0, x0, 0, x2) -> c17(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)), TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))), TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
   IF(even, 0, x0, 0, x2) -> c17(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)), TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))), TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1


----------------------------------------

(195) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID))
Split RHS of tuples not part of any SCC
----------------------------------------

(196)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1, c9_1


----------------------------------------

(197) CdtKnowledgeProof (BOTH BOUNDS(ID, ID))
The following tuples could be moved from S to K by knowledge propagation:
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))

----------------------------------------

(198)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1, c9_1


----------------------------------------

(199) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) by 
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, 0, x2) -> c17(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)), TIMESITER(half(s(0)), x0, half(0)), HALF(0))
   IF(even, s(0), x0, s(z0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, half(s(z0))), timesIter(0, x0, s(half(z0)))), TIMESITER(half(s(0)), x0, half(s(z0))), HALF(s(z0)))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))), HALF(s(0)))
   IF(even, s(0), x0, 0, x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))), TIMESITER(half(s(0)), x0, half(0)), HALF(0))
   IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1))

----------------------------------------

(200)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, 0, x2) -> c17(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)), TIMESITER(half(s(0)), x0, half(0)), HALF(0))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))), HALF(s(0)))
   IF(even, s(0), x0, 0, x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))), TIMESITER(half(s(0)), x0, half(0)), HALF(0))
   IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, 0, x2) -> c17(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)), TIMESITER(half(s(0)), x0, half(0)), HALF(0))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))), HALF(s(0)))
   IF(even, s(0), x0, 0, x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))), TIMESITER(half(s(0)), x0, half(0)), HALF(0))
   IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1, c9_1


----------------------------------------

(201) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 3 trailing tuple parts
----------------------------------------

(202)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1))
   IF(even, s(0), x0, 0, x2) -> c17(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)), TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(0), x0, 0, x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))), TIMESITER(half(s(0)), x0, half(0)))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1))
   IF(even, s(0), x0, 0, x2) -> c17(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)), TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(0), x0, 0, x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))), TIMESITER(half(s(0)), x0, half(0)))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1, c9_1


----------------------------------------

(203) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID))
Split RHS of tuples not part of any SCC
----------------------------------------

(204)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1, c9_1, c12_1


----------------------------------------

(205) CdtKnowledgeProof (BOTH BOUNDS(ID, ID))
The following tuples could be moved from S to K by knowledge propagation:
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))

----------------------------------------

(206)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1, c9_1, c12_1


----------------------------------------

(207) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) by 
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, s(z0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(s(z0))), timesIter(s(half(x0)), x1, s(half(z0)))), TIMESITER(half(s(s(x0))), x1, half(s(z0))), HALF(s(z0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(0))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(0))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(0)))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))

----------------------------------------

(208)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(0))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(0))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(0)))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(0))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(0))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(0)))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1, c9_1, c12_1


----------------------------------------

(209) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 3 trailing tuple parts
----------------------------------------

(210)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1, c9_1, c12_1


----------------------------------------

(211) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(x2)), HALF(x2)) by 
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(0))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(z0)), plus(half(s(z0)), x1)), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(0))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(s(0)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(0))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(s(0)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))

----------------------------------------

(212)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(0))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(0))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(s(0)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(0))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(s(0)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(0))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(0))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(s(0)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(0))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(s(0)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1, c9_1, c12_1


----------------------------------------

(213) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 5 trailing tuple parts
----------------------------------------

(214)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1, c9_1, c12_1


----------------------------------------

(215) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0)))) by 
   IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(timesIter(half(x0), z1, s(half(x2))), if(check(half(x0)), half(x0), z1, half(s(s(s(x2)))), plus(half(s(s(s(x2)))), z1))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(x2))), timesIter(half(x0), x1, s(half(s(x2))))), TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, s(half(x2))), timesIter(s(half(z0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0)))))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0))))))
   IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2))))

----------------------------------------

(216)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0)))))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0))))))
   IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2))))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0)))))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0))))))
   IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2))))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1, c9_1, c12_1


----------------------------------------

(217) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2)) by 
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(0, z1, half(x1)), if(check(half(0)), half(0), z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, 0, x2) -> c17(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)), TIMESITER(half(0), x0, half(0)), HALF(0))
   IF(even, 0, x0, s(z0), x2) -> c17(PLUS(timesIter(0, x0, half(s(z0))), timesIter(half(0), x0, s(half(z0)))), TIMESITER(half(0), x0, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, 0, x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))), TIMESITER(half(0), x0, half(0)), HALF(0))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))), HALF(s(0)))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(0, x0, s(half(z0))), timesIter(half(0), x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))

----------------------------------------

(218)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0)))))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0))))))
   IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, 0, x0, 0, x2) -> c17(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)), TIMESITER(half(0), x0, half(0)), HALF(0))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, 0, x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))), TIMESITER(half(0), x0, half(0)), HALF(0))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))), HALF(s(0)))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0)))))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0))))))
   IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, 0, x0, 0, x2) -> c17(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)), TIMESITER(half(0), x0, half(0)), HALF(0))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, 0, x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))), TIMESITER(half(0), x0, half(0)), HALF(0))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))), HALF(s(0)))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1, c9_1, c12_1


----------------------------------------

(219) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 3 trailing tuple parts
----------------------------------------

(220)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0)))))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0))))))
   IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, 0, x2) -> c17(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)), TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))), TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0)))))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0))))))
   IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, 0, x2) -> c17(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)), TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))), TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1, c9_1, c12_1


----------------------------------------

(221) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID))
Split RHS of tuples not part of any SCC
----------------------------------------

(222)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0)))))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0))))))
   IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0)))))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0))))))
   IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1, c9_1, c12_1, c13_1


----------------------------------------

(223) CdtKnowledgeProof (BOTH BOUNDS(ID, ID))
The following tuples could be moved from S to K by knowledge propagation:
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))

----------------------------------------

(224)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0)))))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0))))))
   IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0)))))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0))))))
   IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1, c9_1, c12_1, c13_1


----------------------------------------

(225) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2)) by 
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(0, z1, half(x1)), if(check(half(s(0))), half(s(0)), z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, 0, x2) -> c17(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)), TIMESITER(half(s(0)), x0, half(0)), HALF(0))
   IF(even, s(0), x0, s(z0), x2) -> c17(PLUS(timesIter(0, x0, half(s(z0))), timesIter(half(s(0)), x0, s(half(z0)))), TIMESITER(half(s(0)), x0, half(s(z0))), HALF(s(z0)))
   IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, 0, x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))), TIMESITER(half(s(0)), x0, half(0)), HALF(0))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))), HALF(s(0)))
   IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(0, x0, s(half(z0))), timesIter(half(s(0)), x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0))))

----------------------------------------

(226)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0)))))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0))))))
   IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c17(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)), TIMESITER(half(s(0)), x0, half(0)), HALF(0))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, 0, x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))), TIMESITER(half(s(0)), x0, half(0)), HALF(0))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))), HALF(s(0)))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0)))))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0))))))
   IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, s(0), x0, 0, x2) -> c17(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)), TIMESITER(half(s(0)), x0, half(0)), HALF(0))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, 0, x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))), TIMESITER(half(s(0)), x0, half(0)), HALF(0))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))), HALF(s(0)))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1, c9_1, c12_1, c13_1


----------------------------------------

(227) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 3 trailing tuple parts
----------------------------------------

(228)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0)))))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0))))))
   IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, 0, x2) -> c17(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)), TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))), TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0)))))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0))))))
   IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, 0, x2) -> c17(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)), TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))), TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1, c9_1, c12_1, c13_1


----------------------------------------

(229) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID))
Split RHS of tuples not part of any SCC
----------------------------------------

(230)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0)))))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0))))))
   IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0)))))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0))))))
   IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1, c9_1, c12_1, c13_1, c14_1


----------------------------------------

(231) CdtKnowledgeProof (BOTH BOUNDS(ID, ID))
The following tuples could be moved from S to K by knowledge propagation:
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))

----------------------------------------

(232)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0)))))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0))))))
   IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0)))))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0))))))
   IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c17_3, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1, c9_1, c12_1, c13_1, c14_1


----------------------------------------

(233) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2)) by 
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(s(half(x0)), z1, half(x2)), if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(0))
   IF(even, s(s(x0)), x1, s(z0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(s(z0))), timesIter(half(s(s(x0))), x1, s(half(z0)))), TIMESITER(half(s(s(x0))), x1, half(s(z0))), HALF(s(z0)))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(0))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(0)))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, s(half(z0))), timesIter(half(s(s(x0))), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))

----------------------------------------

(234)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0)))))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0))))))
   IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(0))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(0))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(0)))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0)))))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0))))))
   IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(0))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(0))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(0)))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1, c17_3, c9_1, c12_1, c13_1, c14_1


----------------------------------------

(235) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 3 trailing tuple parts
----------------------------------------

(236)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0)))))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0))))))
   IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0)))))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0))))))
   IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1, c17_3, c9_1, c12_1, c13_1, c14_1


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(237) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0))) by 
   IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)))
   IF(even, 0, x1, 0, x2) -> c17(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)), TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c17(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)), TIMESITER(half(s(0)), x1, half(0)))
   IF(even, s(s(z0)), x1, 0, x2) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)))
   IF(even, x0, z1, 0, x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)))
   IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c17(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)), TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c17(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)), TIMESITER(half(s(0)), x1, half(0)))
   IF(even, s(s(z0)), x1, 0, x2) -> c17(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)))

----------------------------------------

(238)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0)))))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0))))))
   IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)))
   IF(even, 0, x1, 0, x2) -> c17(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)), TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c17(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)), TIMESITER(half(s(0)), x1, half(0)))
   IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c17(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)), TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c17(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)), TIMESITER(half(s(0)), x1, half(0)))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0)))))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0))))))
   IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)))
   IF(even, 0, x1, 0, x2) -> c17(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)), TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c17(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)), TIMESITER(half(s(0)), x1, half(0)))
   IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c17(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)), TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c17(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)), TIMESITER(half(s(0)), x1, half(0)))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1, c17_3, c9_1, c12_1, c13_1, c14_1


----------------------------------------

(239) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID))
Split RHS of tuples not part of any SCC
----------------------------------------

(240)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0)))))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0))))))
   IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)))
   IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c20(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c20(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0)))))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0))))))
   IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)))
   IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c20(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c20(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1, c17_3, c9_1, c12_1, c13_1, c14_1, c20_1


----------------------------------------

(241) CdtKnowledgeProof (BOTH BOUNDS(ID, ID))
The following tuples could be moved from S to K by knowledge propagation:
   IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c20(TIMESITER(half(0), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c20(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c20(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c20(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))

----------------------------------------

(242)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0)))))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0))))))
   IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)))
   IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c20(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c20(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0)))))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0))))))
   IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)))
   IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c20(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c20(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1, c17_3, c9_1, c12_1, c13_1, c14_1, c20_1


----------------------------------------

(243) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0))) by 
   IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, 0), if(check(half(x0)), half(x0), z1, half(s(0)), plus(half(s(0)), z1))), TIMESITER(half(x0), z1, half(0)))
   IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c17(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))), TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c17(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))), TIMESITER(half(s(0)), x1, half(0)))
   IF(even, s(s(z0)), x1, 0, x2) -> c17(PLUS(timesIter(half(s(s(z0))), x1, 0), timesIter(s(half(z0)), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)))
   IF(even, x0, z1, 0, x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)))
   IF(even, 0, x1, 0, x2) -> c17(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))), TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c17(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))), TIMESITER(half(s(0)), x1, half(0)))
   IF(even, s(s(z0)), x1, 0, x2) -> c17(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)))

----------------------------------------

(244)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0)))))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0))))))
   IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)))
   IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c20(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c20(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, 0, x1, 0, x2) -> c17(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))), TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c17(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))), TIMESITER(half(s(0)), x1, half(0)))
   IF(even, x0, z1, 0, x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)))
   IF(even, 0, x1, 0, x2) -> c17(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))), TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c17(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))), TIMESITER(half(s(0)), x1, half(0)))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0)))))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0))))))
   IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)))
   IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c17(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))), TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c17(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))), TIMESITER(half(s(0)), x1, half(0)))
   IF(even, x0, z1, 0, x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)))
   IF(even, 0, x1, 0, x2) -> c17(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))), TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c17(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))), TIMESITER(half(s(0)), x1, half(0)))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c20(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c20(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1, c17_3, c9_1, c12_1, c13_1, c14_1, c20_1


----------------------------------------

(245) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID))
Split RHS of tuples not part of any SCC
----------------------------------------

(246)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0)))))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0))))))
   IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)))
   IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c20(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c20(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, 0, x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)))
   IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c21(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c21(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0)))))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0))))))
   IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)))
   IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, z1, 0, x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)))
   IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c21(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c21(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c20(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c20(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1, c17_3, c9_1, c12_1, c13_1, c14_1, c20_1, c21_1


----------------------------------------

(247) CdtKnowledgeProof (BOTH BOUNDS(ID, ID))
The following tuples could be moved from S to K by knowledge propagation:
   IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c21(TIMESITER(half(0), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c21(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c21(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c21(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))

----------------------------------------

(248)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0)))))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0))))))
   IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)))
   IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c20(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c20(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, 0, x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)))
   IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c21(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c21(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0)))))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0))))))
   IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)))
   IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, z1, 0, x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c20(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c20(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c21(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c21(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c17_2, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1, c17_3, c9_1, c12_1, c13_1, c14_1, c20_1, c21_1


----------------------------------------

(249) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0)))) by 
   IF(even, x0, z1, s(0), x2) -> c17(PLUS(timesIter(half(x0), z1, 0), if(check(half(x0)), half(x0), z1, half(s(s(0))), plus(half(s(s(0))), z1))), TIMESITER(half(x0), z1, half(s(0))))
   IF(even, x0, x1, s(0), x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c17(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, s(s(z0)), x1, s(0), x2) -> c17(PLUS(timesIter(half(s(s(z0))), x1, 0), timesIter(s(half(z0)), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))))
   IF(even, x0, z1, s(0), x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c17(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c17(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, s(s(z0)), x1, s(0), x2) -> c17(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))))
   IF(even, x0, x1, s(0), x2) -> c17(TIMESITER(half(x0), x1, half(s(0))))

----------------------------------------

(250)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0)))))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0))))))
   IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)))
   IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c20(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c20(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, 0, x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)))
   IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c21(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c21(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, x0, z1, s(0), x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))))
   IF(even, x0, x1, s(0), x2) -> c17(TIMESITER(half(x0), x1, half(s(0))))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0)))))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0))))))
   IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)))
   IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, z1, 0, x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)))
   IF(even, x0, z1, s(0), x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))))
   IF(even, x0, x1, s(0), x2) -> c17(TIMESITER(half(x0), x1, half(s(0))))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c20(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c20(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c21(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c21(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1, c17_3, c17_2, c9_1, c12_1, c13_1, c14_1, c20_1, c21_1, c17_1


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(251) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace IF(even, x0, z1, x2, x3) -> c18(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) by 
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))), HALF(0))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(0)))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))), HALF(0))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(0)))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))), HALF(0))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(0)))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))

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(252)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0)))))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0))))))
   IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)))
   IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c20(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c20(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, 0, x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)))
   IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c21(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c21(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, x0, z1, s(0), x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))))
   IF(even, x0, x1, s(0), x2) -> c17(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))), HALF(0))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(0)))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))), HALF(0))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(0)))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))), HALF(0))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(0)))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0)))))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0))))))
   IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)))
   IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, z1, 0, x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)))
   IF(even, x0, z1, s(0), x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))))
   IF(even, x0, x1, s(0), x2) -> c17(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))), HALF(0))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(0)))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))), HALF(0))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(0)))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))), HALF(0))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(0)))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c20(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c20(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c21(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c21(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1, c17_3, c17_2, c9_1, c12_1, c13_1, c14_1, c20_1, c21_1, c17_1


----------------------------------------

(253) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 6 trailing tuple parts
----------------------------------------

(254)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0)))))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0))))))
   IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)))
   IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c20(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c20(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, 0, x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)))
   IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c21(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c21(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, x0, z1, s(0), x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))))
   IF(even, x0, x1, s(0), x2) -> c17(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0)))))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0))))))
   IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)))
   IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, z1, 0, x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)))
   IF(even, x0, z1, s(0), x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))))
   IF(even, x0, x1, s(0), x2) -> c17(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c20(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c20(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c21(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c21(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1, c17_3, c17_2, c9_1, c12_1, c13_1, c14_1, c20_1, c21_1, c17_1


----------------------------------------

(255) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) by 
   IF(even, x0, z1, 0, x2) -> c18(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, 0, x1, 0, x2) -> c18(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)), TIMESITER(half(0), x1, half(s(0))), HALF(0))
   IF(even, s(0), x1, 0, x2) -> c18(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)), TIMESITER(half(s(0)), x1, half(s(0))), HALF(s(0)))
   IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, 0, x1, 0, x2) -> c18(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)), TIMESITER(half(0), x1, half(s(0))), HALF(0))
   IF(even, s(0), x1, 0, x2) -> c18(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)), TIMESITER(half(s(0)), x1, half(s(0))), HALF(s(0)))
   IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))

----------------------------------------

(256)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0)))))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0))))))
   IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)))
   IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c20(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c20(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, 0, x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)))
   IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c21(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c21(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, x0, z1, s(0), x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))))
   IF(even, x0, x1, s(0), x2) -> c17(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, 0, x2) -> c18(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, 0, x1, 0, x2) -> c18(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)), TIMESITER(half(0), x1, half(s(0))), HALF(0))
   IF(even, s(0), x1, 0, x2) -> c18(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)), TIMESITER(half(s(0)), x1, half(s(0))), HALF(s(0)))
   IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, 0, x1, 0, x2) -> c18(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)), TIMESITER(half(0), x1, half(s(0))), HALF(0))
   IF(even, s(0), x1, 0, x2) -> c18(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)), TIMESITER(half(s(0)), x1, half(s(0))), HALF(s(0)))
   IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0)))))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0))))))
   IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)))
   IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, z1, 0, x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)))
   IF(even, x0, z1, s(0), x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))))
   IF(even, x0, x1, s(0), x2) -> c17(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, 0, x2) -> c18(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, 0, x1, 0, x2) -> c18(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)), TIMESITER(half(0), x1, half(s(0))), HALF(0))
   IF(even, s(0), x1, 0, x2) -> c18(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)), TIMESITER(half(s(0)), x1, half(s(0))), HALF(s(0)))
   IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, 0, x1, 0, x2) -> c18(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)), TIMESITER(half(0), x1, half(s(0))), HALF(0))
   IF(even, s(0), x1, 0, x2) -> c18(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)), TIMESITER(half(s(0)), x1, half(s(0))), HALF(s(0)))
   IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c20(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c20(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c21(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c21(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1, c17_3, c17_2, c9_1, c12_1, c13_1, c14_1, c20_1, c21_1, c17_1


----------------------------------------

(257) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 4 trailing tuple parts
----------------------------------------

(258)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0)))))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0))))))
   IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)))
   IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c20(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c20(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, 0, x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)))
   IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c21(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c21(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, x0, z1, s(0), x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))))
   IF(even, x0, x1, s(0), x2) -> c17(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, 0, x2) -> c18(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c18(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, 0, x2) -> c18(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, 0, x2) -> c18(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, 0, x2) -> c18(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)), TIMESITER(half(s(0)), x1, half(s(0))))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0)))))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0))))))
   IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)))
   IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, z1, 0, x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)))
   IF(even, x0, z1, s(0), x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))))
   IF(even, x0, x1, s(0), x2) -> c17(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, 0, x2) -> c18(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c18(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, 0, x2) -> c18(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, 0, x2) -> c18(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, 0, x2) -> c18(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)), TIMESITER(half(s(0)), x1, half(s(0))))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c20(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c20(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c21(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c21(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1, c17_3, c17_2, c9_1, c12_1, c13_1, c14_1, c20_1, c21_1, c17_1


----------------------------------------

(259) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID))
Split RHS of tuples not part of any SCC
----------------------------------------

(260)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0)))))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0))))))
   IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)))
   IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c20(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c20(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, 0, x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)))
   IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c21(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c21(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, x0, z1, s(0), x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))))
   IF(even, x0, x1, s(0), x2) -> c17(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, 0, x2) -> c18(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c22(TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c22(TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0)))))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0))))))
   IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)))
   IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, z1, 0, x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)))
   IF(even, x0, z1, s(0), x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))))
   IF(even, x0, x1, s(0), x2) -> c17(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, 0, x2) -> c18(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c22(TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c22(TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c20(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c20(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c21(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c21(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1, c17_3, c17_2, c9_1, c12_1, c13_1, c14_1, c20_1, c21_1, c17_1, c22_1


----------------------------------------

(261) CdtKnowledgeProof (BOTH BOUNDS(ID, ID))
The following tuples could be moved from S to K by knowledge propagation:
   IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c22(TIMESITER(half(0), x1, half(s(0))))
   IF(even, 0, x1, 0, x2) -> c22(TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c22(TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, s(0), x1, 0, x2) -> c22(TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))

----------------------------------------

(262)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0)))))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0))))))
   IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)))
   IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c20(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c20(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, 0, x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)))
   IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c21(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c21(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, x0, z1, s(0), x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))))
   IF(even, x0, x1, s(0), x2) -> c17(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, 0, x2) -> c18(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c22(TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c22(TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0)))))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0))))))
   IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)))
   IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, z1, 0, x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)))
   IF(even, x0, z1, s(0), x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))))
   IF(even, x0, x1, s(0), x2) -> c17(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, 0, x2) -> c18(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c20(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c20(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c21(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c21(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c22(TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c22(TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1, c17_3, c17_2, c9_1, c12_1, c13_1, c14_1, c20_1, c21_1, c17_1, c22_1


----------------------------------------

(263) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0)) by 
   IF(even, x0, z1, s(x2), x3) -> c18(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, 0, x1, s(x2), x3) -> c18(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(0))
   IF(even, s(0), x1, s(x2), x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(0)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, 0, x1, s(x2), x3) -> c18(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(0))
   IF(even, s(0), x1, s(x2), x3) -> c18(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(0)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(x2), x3) -> c18(TIMESITER(half(x0), x1, half(s(s(x2)))))

----------------------------------------

(264)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0)))))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0))))))
   IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)))
   IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c20(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c20(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, 0, x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)))
   IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c21(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c21(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, x0, z1, s(0), x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))))
   IF(even, x0, x1, s(0), x2) -> c17(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, 0, x2) -> c18(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c22(TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c22(TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, s(x2), x3) -> c18(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, 0, x1, s(x2), x3) -> c18(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(0))
   IF(even, s(0), x1, s(x2), x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(0)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, 0, x1, s(x2), x3) -> c18(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(0))
   IF(even, s(0), x1, s(x2), x3) -> c18(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(0)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(x2), x3) -> c18(TIMESITER(half(x0), x1, half(s(s(x2)))))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0)))))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0))))))
   IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)))
   IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, z1, 0, x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)))
   IF(even, x0, z1, s(0), x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))))
   IF(even, x0, x1, s(0), x2) -> c17(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, 0, x2) -> c18(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c18(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, 0, x1, s(x2), x3) -> c18(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(0))
   IF(even, s(0), x1, s(x2), x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(0)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, 0, x1, s(x2), x3) -> c18(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(0))
   IF(even, s(0), x1, s(x2), x3) -> c18(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(0)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(x2), x3) -> c18(TIMESITER(half(x0), x1, half(s(s(x2)))))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c20(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c20(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c21(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c21(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c22(TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c22(TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1, c17_3, c17_2, c9_1, c12_1, c13_1, c14_1, c20_1, c21_1, c17_1, c22_1, c18_1


----------------------------------------

(265) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 4 trailing tuple parts
----------------------------------------

(266)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0)))))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0))))))
   IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)))
   IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c20(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c20(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, 0, x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)))
   IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c21(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c21(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, x0, z1, s(0), x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))))
   IF(even, x0, x1, s(0), x2) -> c17(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, 0, x2) -> c18(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c22(TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c22(TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, s(x2), x3) -> c18(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(x2), x3) -> c18(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(x2), x3) -> c18(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(x2), x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(x2), x3) -> c18(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(x2), x3) -> c18(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0)))))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0))))))
   IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)))
   IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, z1, 0, x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)))
   IF(even, x0, z1, s(0), x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))))
   IF(even, x0, x1, s(0), x2) -> c17(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, 0, x2) -> c18(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c18(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(x2), x3) -> c18(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(x2), x3) -> c18(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(x2), x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(x2), x3) -> c18(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(x2), x3) -> c18(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c20(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c20(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c21(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c21(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c22(TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c22(TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1, c17_3, c17_2, c9_1, c12_1, c13_1, c14_1, c20_1, c21_1, c17_1, c22_1, c18_1


----------------------------------------

(267) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0)))) by 
   IF(even, s(s(x0)), z1, x2, x3) -> c18(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(s(x2))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(z0), x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, half(s(z0))), timesIter(s(half(x0)), x1, s(half(z0)))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(s(x2))), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(s(x2))), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(s(x2))), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c18(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(s(x2))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(s(z0))))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(s(0)))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))

----------------------------------------

(268)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0)))))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0))))))
   IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)))
   IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c20(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c20(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, 0, x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)))
   IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c21(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c21(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, x0, z1, s(0), x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))))
   IF(even, x0, x1, s(0), x2) -> c17(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, 0, x2) -> c18(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c22(TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c22(TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, s(x2), x3) -> c18(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(x2), x3) -> c18(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(x2), x3) -> c18(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(x2), x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(x2), x3) -> c18(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(x2), x3) -> c18(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c18(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(s(x2))), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(s(x2))), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(s(x2))), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(s(x2))), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c18(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(s(x2))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(s(z0))))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(s(0)))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0)))))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0))))))
   IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)))
   IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, z1, 0, x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)))
   IF(even, x0, z1, s(0), x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))))
   IF(even, x0, x1, s(0), x2) -> c17(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, 0, x2) -> c18(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c18(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(x2), x3) -> c18(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(x2), x3) -> c18(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(x2), x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(x2), x3) -> c18(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(x2), x3) -> c18(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c18(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(s(x2))), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(s(x2))), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(s(x2))), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(s(x2))), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c18(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(s(x2))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(s(z0))))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(s(0)))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c20(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c20(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c21(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c21(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c22(TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c22(TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1, c17_3, c17_2, c9_1, c12_1, c13_1, c14_1, c20_1, c21_1, c17_1, c22_1, c18_1


----------------------------------------

(269) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0)) by 
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, half(s(z0)), plus(half(s(z0)), x1)), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(0))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(0)))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(0))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(0)))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(0))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(0)))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))

----------------------------------------

(270)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0)))))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0))))))
   IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)))
   IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c20(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c20(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, 0, x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)))
   IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c21(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c21(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, x0, z1, s(0), x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))))
   IF(even, x0, x1, s(0), x2) -> c17(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, 0, x2) -> c18(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c22(TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c22(TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, s(x2), x3) -> c18(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(x2), x3) -> c18(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(x2), x3) -> c18(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(x2), x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(x2), x3) -> c18(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(x2), x3) -> c18(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c18(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(s(x2))), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(s(x2))), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(s(x2))), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(s(x2))), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c18(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(s(x2))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(s(z0))))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(s(0)))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(0))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(0)))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(0))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(0)))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(0))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(0)))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0)))))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0))))))
   IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)))
   IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, z1, 0, x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)))
   IF(even, x0, z1, s(0), x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))))
   IF(even, x0, x1, s(0), x2) -> c17(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, 0, x2) -> c18(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c18(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(x2), x3) -> c18(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(x2), x3) -> c18(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(x2), x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(x2), x3) -> c18(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(x2), x3) -> c18(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c18(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(s(x2))), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(s(x2))), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(s(x2))), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(s(x2))), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c18(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(s(x2))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(s(z0))))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(s(0)))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(0))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(0)))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(0))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(0)))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(0))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(0)))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c20(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c20(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c21(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c21(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c22(TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c22(TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1, c17_3, c17_2, c9_1, c12_1, c13_1, c14_1, c20_1, c21_1, c17_1, c22_1, c18_1


----------------------------------------

(271) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 6 trailing tuple parts
----------------------------------------

(272)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0)))))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0))))))
   IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)))
   IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c20(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c20(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, 0, x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)))
   IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c21(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c21(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, x0, z1, s(0), x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))))
   IF(even, x0, x1, s(0), x2) -> c17(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, 0, x2) -> c18(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c22(TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c22(TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, s(x2), x3) -> c18(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(x2), x3) -> c18(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(x2), x3) -> c18(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(x2), x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(x2), x3) -> c18(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(x2), x3) -> c18(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c18(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(s(x2))), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(s(x2))), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(s(x2))), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(s(x2))), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c18(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(s(x2))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(s(z0))))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(s(0)))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0)))))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0))))))
   IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)))
   IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, z1, 0, x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)))
   IF(even, x0, z1, s(0), x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))))
   IF(even, x0, x1, s(0), x2) -> c17(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, 0, x2) -> c18(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c18(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(x2), x3) -> c18(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(x2), x3) -> c18(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(x2), x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(x2), x3) -> c18(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(x2), x3) -> c18(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c18(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(s(x2))), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(s(x2))), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(s(x2))), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(s(x2))), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c18(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(s(x2))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(s(z0))))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(s(0)))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c20(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c20(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c21(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c21(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c22(TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c22(TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1, c17_3, c17_2, c9_1, c12_1, c13_1, c14_1, c20_1, c21_1, c17_1, c22_1, c18_1


----------------------------------------

(273) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0)) by 
   IF(even, x0, z1, 0, x2) -> c18(PLUS(timesIter(half(x0), z1, 0), if(check(half(x0)), half(x0), z1, half(s(0)), plus(half(s(0)), z1))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, 0, x1, 0, x2) -> c18(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))), TIMESITER(half(0), x1, half(s(0))), HALF(0))
   IF(even, s(0), x1, 0, x2) -> c18(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))), TIMESITER(half(s(0)), x1, half(s(0))), HALF(s(0)))
   IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(half(s(s(z0))), x1, 0), timesIter(s(half(z0)), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c18(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, 0, x1, 0, x2) -> c18(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))), TIMESITER(half(0), x1, half(s(0))), HALF(0))
   IF(even, s(0), x1, 0, x2) -> c18(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))), TIMESITER(half(s(0)), x1, half(s(0))), HALF(s(0)))
   IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))

----------------------------------------

(274)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0)))))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0))))))
   IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)))
   IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c20(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c20(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, 0, x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)))
   IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c21(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c21(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, x0, z1, s(0), x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))))
   IF(even, x0, x1, s(0), x2) -> c17(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, 0, x2) -> c18(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c22(TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c22(TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, s(x2), x3) -> c18(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(x2), x3) -> c18(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(x2), x3) -> c18(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(x2), x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(x2), x3) -> c18(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(x2), x3) -> c18(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c18(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(s(x2))), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(s(x2))), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(s(x2))), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(s(x2))), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c18(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(s(x2))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(s(z0))))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(s(0)))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, 0, x2) -> c18(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))), TIMESITER(half(0), x1, half(s(0))), HALF(0))
   IF(even, s(0), x1, 0, x2) -> c18(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))), TIMESITER(half(s(0)), x1, half(s(0))), HALF(s(0)))
   IF(even, x0, z1, 0, x2) -> c18(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, 0, x1, 0, x2) -> c18(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))), TIMESITER(half(0), x1, half(s(0))), HALF(0))
   IF(even, s(0), x1, 0, x2) -> c18(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))), TIMESITER(half(s(0)), x1, half(s(0))), HALF(s(0)))
   IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0)))))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0))))))
   IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)))
   IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, z1, 0, x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)))
   IF(even, x0, z1, s(0), x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))))
   IF(even, x0, x1, s(0), x2) -> c17(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, 0, x2) -> c18(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c18(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(x2), x3) -> c18(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(x2), x3) -> c18(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(x2), x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(x2), x3) -> c18(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(x2), x3) -> c18(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c18(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(s(x2))), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(s(x2))), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(s(x2))), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(s(x2))), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c18(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(s(x2))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(s(z0))))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(s(0)))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, 0, x2) -> c18(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))), TIMESITER(half(0), x1, half(s(0))), HALF(0))
   IF(even, s(0), x1, 0, x2) -> c18(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))), TIMESITER(half(s(0)), x1, half(s(0))), HALF(s(0)))
   IF(even, x0, z1, 0, x2) -> c18(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, 0, x1, 0, x2) -> c18(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))), TIMESITER(half(0), x1, half(s(0))), HALF(0))
   IF(even, s(0), x1, 0, x2) -> c18(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))), TIMESITER(half(s(0)), x1, half(s(0))), HALF(s(0)))
   IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c20(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c20(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c21(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c21(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c22(TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c22(TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1, c17_3, c17_2, c9_1, c12_1, c13_1, c14_1, c20_1, c21_1, c17_1, c22_1, c18_1


----------------------------------------

(275) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 4 trailing tuple parts
----------------------------------------

(276)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0)))))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0))))))
   IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)))
   IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c20(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c20(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, 0, x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)))
   IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c21(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c21(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, x0, z1, s(0), x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))))
   IF(even, x0, x1, s(0), x2) -> c17(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, 0, x2) -> c18(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c22(TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c22(TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, s(x2), x3) -> c18(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(x2), x3) -> c18(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(x2), x3) -> c18(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(x2), x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(x2), x3) -> c18(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(x2), x3) -> c18(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c18(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(s(x2))), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(s(x2))), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(s(x2))), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(s(x2))), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c18(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(s(x2))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(s(z0))))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(s(0)))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, 0, x2) -> c18(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c18(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, 0, x2) -> c18(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, 0, x2) -> c18(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, 0, x2) -> c18(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))), TIMESITER(half(s(0)), x1, half(s(0))))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0)))))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0))))))
   IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)))
   IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, z1, 0, x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)))
   IF(even, x0, z1, s(0), x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))))
   IF(even, x0, x1, s(0), x2) -> c17(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, 0, x2) -> c18(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c18(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(x2), x3) -> c18(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(x2), x3) -> c18(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(x2), x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(x2), x3) -> c18(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(x2), x3) -> c18(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c18(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(s(x2))), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(s(x2))), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(s(x2))), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(s(x2))), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c18(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(s(x2))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(s(z0))))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(s(0)))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, 0, x2) -> c18(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c18(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, 0, x2) -> c18(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, 0, x2) -> c18(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, 0, x2) -> c18(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))), TIMESITER(half(s(0)), x1, half(s(0))))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c20(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c20(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c21(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c21(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c22(TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c22(TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1, c17_3, c17_2, c9_1, c12_1, c13_1, c14_1, c20_1, c21_1, c17_1, c22_1, c18_1


----------------------------------------

(277) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID))
Split RHS of tuples not part of any SCC
----------------------------------------

(278)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0)))))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0))))))
   IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)))
   IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c20(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c20(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, 0, x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)))
   IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c21(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c21(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, x0, z1, s(0), x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))))
   IF(even, x0, x1, s(0), x2) -> c17(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, 0, x2) -> c18(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c22(TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c22(TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, s(x2), x3) -> c18(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(x2), x3) -> c18(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(x2), x3) -> c18(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(x2), x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(x2), x3) -> c18(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(x2), x3) -> c18(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c18(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(s(x2))), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(s(x2))), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(s(x2))), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(s(x2))), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c18(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(s(x2))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(s(z0))))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(s(0)))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, 0, x2) -> c18(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c23(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c23(TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, 0, x2) -> c23(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c23(TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, 0, x2) -> c23(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c23(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0)))))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0))))))
   IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)))
   IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, z1, 0, x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)))
   IF(even, x0, z1, s(0), x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))))
   IF(even, x0, x1, s(0), x2) -> c17(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, 0, x2) -> c18(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c18(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(x2), x3) -> c18(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(x2), x3) -> c18(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(x2), x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(x2), x3) -> c18(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(x2), x3) -> c18(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c18(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(s(x2))), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(s(x2))), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(s(x2))), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(s(x2))), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c18(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(s(x2))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(s(z0))))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(s(0)))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, 0, x2) -> c18(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c23(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c23(TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, 0, x2) -> c23(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c23(TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, 0, x2) -> c23(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c23(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c20(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c20(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c21(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c21(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c22(TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c22(TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1, c17_3, c17_2, c9_1, c12_1, c13_1, c14_1, c20_1, c21_1, c17_1, c22_1, c18_1, c23_1


----------------------------------------

(279) CdtKnowledgeProof (BOTH BOUNDS(ID, ID))
The following tuples could be moved from S to K by knowledge propagation:
   IF(even, 0, x1, 0, x2) -> c23(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c23(TIMESITER(half(0), x1, half(s(0))))
   IF(even, 0, x1, 0, x2) -> c23(TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, 0, x2) -> c23(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c23(TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, s(0), x1, 0, x2) -> c23(TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, 0, x2) -> c23(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c23(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))

----------------------------------------

(280)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   check(0) -> zero
   check(s(0)) -> odd
   check(s(s(0))) -> even
   check(s(s(s(z0)))) -> check(s(z0))
   plus(0, z0) -> z0
   plus(s(z0), z1) -> s(plus(z0, z1))
   timesIter(z0, z1, z2) -> if(check(z0), z0, z1, z2, plus(z2, z1))
   half(0) -> 0
   half(s(0)) -> 0
   half(s(s(z0))) -> s(half(z0))
   if(zero, z0, z1, z2, z3) -> z2
   if(odd, z0, z1, z2, z3) -> timesIter(p(z0), z1, z3)
   if(even, z0, z1, z2, z3) -> plus(timesIter(half(z0), z1, half(z2)), timesIter(half(z0), z1, half(s(z2))))
   p(s(z0)) -> z0
   p(0) -> 0
Tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0)))))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0))))))
   IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)))
   IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c20(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c20(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, 0, x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)))
   IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c21(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c21(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, x0, z1, s(0), x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))))
   IF(even, x0, x1, s(0), x2) -> c17(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, 0, x2) -> c18(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c22(TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c22(TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, x0, z1, s(x2), x3) -> c18(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(x2), x3) -> c18(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(x2), x3) -> c18(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(x2), x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(x2), x3) -> c18(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(x2), x3) -> c18(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c18(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(s(x2))), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(s(x2))), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(s(x2))), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(s(x2))), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c18(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(s(x2))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(s(z0))))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(s(0)))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, 0, x2) -> c18(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, 0, x1, 0, x2) -> c23(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c23(TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, 0, x2) -> c23(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c23(TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, 0, x2) -> c23(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c23(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
S tuples:
   CHECK(s(s(s(z0)))) -> c3(CHECK(s(z0)))
   HALF(s(s(z0))) -> c6(HALF(z0))
   PLUS(s(z0), z1) -> c8(PLUS(z0, z1))
   IF(odd, z0, z1, z2, z3) -> c15(TIMESITER(p(z0), z1, z3))
   TIMESITER(s(0), x1, x2) -> c10(IF(odd, s(0), x1, x2, plus(x2, x1)))
   TIMESITER(s(s(0)), x1, x2) -> c10(IF(even, s(s(0)), x1, x2, plus(x2, x1)))
   TIMESITER(s(0), x1, x2) -> c11(IF(odd, s(0), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(0)), x1, x2) -> c11(IF(even, s(s(0)), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(timesIter(half(x0), z1, half(x2)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(z0), x3) -> c19(PLUS(timesIter(half(x0), x1, half(s(z0))), timesIter(half(x0), x1, s(half(z0)))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(half(0), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(half(s(0)), x1, half(x2)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, x2, x3) -> c19(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), timesIter(half(x0), z1, half(s(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c19(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, x2, x3) -> c19(PLUS(timesIter(0, x1, half(x2)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, x2, x3) -> c19(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, half(0)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c19(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))))
   TIMESITER(s(s(s(z0))), x1, 0) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, 0, x1), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, 0) -> c10(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c10(IF(even, s(s(0)), x1, 0, x1))
   TIMESITER(x0, z0, s(0)) -> c10(IF(check(x0), x0, z0, s(0), s(z0)), CHECK(x0))
   TIMESITER(x0, z1, s(s(z0))) -> c10(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), CHECK(x0))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c10(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), CHECK(s(s(s(z0)))))
   TIMESITER(s(0), x1, s(x2)) -> c10(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(0)), x1, s(x2)) -> c10(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))))
   TIMESITER(s(s(s(0))), x1, x2) -> c10(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), CHECK(s(s(s(0)))))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c10(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(0))))))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c10(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), CHECK(s(s(s(s(s(z0)))))))
   TIMESITER(x0, z0, s(0)) -> c11(IF(check(x0), x0, z0, s(0), s(z0)), PLUS(s(0), z0))
   TIMESITER(x0, z1, s(s(z0))) -> c11(IF(check(x0), x0, z1, s(s(z0)), s(s(plus(z0, z1)))), PLUS(s(s(z0)), z1))
   TIMESITER(s(0), x1, s(x2)) -> c11(IF(odd, s(0), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(0)), x1, s(x2)) -> c11(IF(even, s(s(0)), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(z0))), x1, s(x2)) -> c11(IF(check(s(z0)), s(s(s(z0))), x1, s(x2), s(plus(x2, x1))), PLUS(s(x2), x1))
   TIMESITER(s(s(s(0))), x1, x2) -> c11(IF(odd, s(s(s(0))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(0)))), x1, x2) -> c11(IF(even, s(s(s(s(0)))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(s(s(z0))))), x1, x2) -> c11(IF(check(s(z0)), s(s(s(s(s(z0))))), x1, x2, plus(x2, x1)), PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), z0, 0) -> c11(IF(check(s(x0)), s(s(s(x0))), z0, 0, z0))
   TIMESITER(s(0), x1, 0) -> c11(IF(odd, s(0), x1, 0, x1))
   TIMESITER(s(s(0)), x1, 0) -> c11(IF(even, s(s(0)), x1, 0, x1))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c16(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, s(x2), x3) -> c16(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c16(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c16(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, 0, x1, x2, x3) -> c16(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)))
   IF(even, s(0), x1, x2, x3) -> c16(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)))
   IF(even, x0, z1, 0, x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(0)), HALF(s(s(z0))))
   IF(even, x0, z1, s(0), x2) -> c16(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, s(0), x2) -> c16(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(s(0))))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, x1, s(0), x2) -> c16(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(s(0))))), TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, s(0), x2) -> c16(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(s(0))))), TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c16(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(s(0))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c16(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(x2)), x3) -> c16(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(0), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(half(s(0)), x1, s(half(x2))), timesIter(0, x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c16(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c16(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(s(s(x0))))
   IF(even, s(s(0)), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c16(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(s(s(s(0)))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c16(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(s(s(s(s(z0))))))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)))
   IF(even, 0, x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, s(0), x0, x1, x2) -> c16(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)))
   IF(even, 0, z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)))
   IF(even, s(0), z1, x1, x2) -> c16(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, x0, x1, s(z0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(z0))), HALF(s(z0)))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, z1, x2, x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(x2)), HALF(x2))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(s(s(s(z0)))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, z1, s(x2), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(0), x1, s(x2), x3) -> c17(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))), HALF(s(x2)))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(x2)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(timesIter(half(0), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(half(0)), half(0), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(0), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(0), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(0), x0, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(timesIter(half(s(0)), z1, half(x1)), if(check(0), 0, z1, half(s(x1)), plus(half(s(x1)), z1))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(half(s(0))), half(s(0)), z1, half(x1), plus(half(x1), z1)), timesIter(0, z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(s(z0)), x2) -> c17(PLUS(timesIter(half(s(0)), x0, s(half(z0))), timesIter(0, x0, half(s(s(s(z0)))))), TIMESITER(half(s(0)), x0, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(0), x0, x1, x2) -> c17(PLUS(timesIter(0, x0, half(x1)), timesIter(0, x0, half(s(x1)))), TIMESITER(half(s(0)), x0, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, half(0)), timesIter(s(half(x0)), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(s(z0)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, 0, x1, x2, x3) -> c17(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(x2)), HALF(x2))
   IF(even, s(0), x1, x2, x3) -> c17(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(x2)), HALF(x2))
   IF(even, s(s(z0)), x1, x2, x3) -> c17(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(x2)), HALF(x2))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(half(0), x1)), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, x1, s(0), x3) -> c17(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, z1, s(s(x2)), x3) -> c17(PLUS(if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1)), timesIter(half(x0), z1, half(s(s(s(x2)))))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(0)), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(0)))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(s(s(0))))
   IF(even, x0, x1, s(s(s(0))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(0)), timesIter(half(x0), x1, half(s(s(s(s(0))))))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(s(s(s(0)))))
   IF(even, x0, x1, s(s(s(s(z0)))), x3) -> c17(PLUS(timesIter(half(x0), x1, s(s(half(z0)))), timesIter(half(x0), x1, half(s(s(s(s(s(z0)))))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(s(s(s(s(z0))))))
   IF(even, 0, x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(0), x1, half(s(s(s(x2)))))), TIMESITER(half(0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(0), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(0, x1, s(half(x2))), timesIter(half(s(0)), x1, half(s(s(s(x2)))))), TIMESITER(half(s(0)), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, s(s(z0)), x1, s(s(x2)), x3) -> c17(PLUS(timesIter(s(half(z0)), x1, s(half(x2))), timesIter(half(s(s(z0))), x1, half(s(s(s(x2)))))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, x0, x1, s(s(x2)), x3) -> c17(TIMESITER(half(x0), x1, half(s(s(x2)))), HALF(s(s(x2))))
   IF(even, 0, z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(0), z1, half(s(x1)))), TIMESITER(half(0), z1, half(x1)), HALF(x1))
   IF(even, 0, x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(s(0))))), TIMESITER(half(0), x0, half(s(0))))
   IF(even, s(0), z1, x1, x2) -> c17(PLUS(if(check(0), 0, z1, half(x1), plus(half(x1), z1)), timesIter(half(s(0)), z1, half(s(x1)))), TIMESITER(half(s(0)), z1, half(x1)), HALF(x1))
   IF(even, s(0), x0, s(0), x2) -> c17(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(s(0))))), TIMESITER(half(s(0)), x0, half(s(0))))
   IF(even, s(s(x0)), z1, x2, x3) -> c17(PLUS(if(check(s(half(x0))), s(half(x0)), z1, half(x2), plus(half(x2), z1)), timesIter(half(s(s(x0))), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(x2)), HALF(x2))
   IF(even, s(s(0)), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(0))), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(0))), x1, x2, x3) -> c17(PLUS(timesIter(s(0), x1, half(x2)), timesIter(half(s(s(s(0)))), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(x2)), HALF(x2))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c17(PLUS(timesIter(s(s(half(z0))), x1, half(x2)), timesIter(half(s(s(s(s(z0))))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(x2)), HALF(x2))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, half(0)), timesIter(half(s(s(x0))), x1, 0)), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, 0, x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(0)))
   IF(even, s(s(x0)), x1, s(0), x3) -> c17(PLUS(timesIter(s(half(x0)), x1, 0), timesIter(half(s(s(x0))), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(0))))
   IF(even, x0, z1, 0, x2) -> c17(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(0)))
   IF(even, x0, x1, 0, x2) -> c17(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(0)))
   IF(even, x0, z1, 0, x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(0)))
   IF(even, x0, z1, s(0), x2) -> c17(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(s(0))))), TIMESITER(half(x0), z1, half(s(0))))
   IF(even, x0, x1, s(0), x2) -> c17(TIMESITER(half(x0), x1, half(s(0))))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, half(0)), if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(z0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(z0))), if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1))), TIMESITER(half(x0), x1, half(s(s(z0)))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(half(s(s(z0)))), s(half(z0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(x2)), if(check(s(half(z0))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, z1, x2, x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(x2), plus(half(x2), z1)), if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(x0), z1, half(s(x2))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(0)), plus(half(s(0)), x1))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), if(check(half(x0)), half(x0), x1, half(s(s(0))), plus(half(s(s(0))), x1))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), if(check(half(x0)), half(x0), x1, half(s(s(s(z0)))), plus(half(s(s(s(z0)))), x1))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), if(check(half(s(s(z0)))), half(s(s(z0))), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(half(0)), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(half(s(0))), 0, x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(half(0), x1, half(x2)), if(check(0), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(x2)), if(check(0), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(0)), half(0), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(timesIter(0, x1, half(x2)), if(check(half(s(0))), half(s(0)), x1, half(s(x2)), plus(half(s(x2)), x1))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, 0, x2) -> c18(PLUS(timesIter(half(x0), z1, half(0)), if(check(half(x0)), half(x0), z1, 0, plus(0, z1))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(0)), timesIter(s(half(z0)), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, z1, 0, x2) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(0), plus(half(0), z1)), timesIter(half(x0), z1, 0)), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, x0, x1, 0, x2) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, 0)), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(s(half(z0)), x1, half(0)), timesIter(half(s(s(z0))), x1, 0)), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c18(PLUS(timesIter(half(x0), z1, half(s(x2))), if(check(half(x0)), half(x0), z1, s(half(x2)), plus(s(half(x2)), z1))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(0))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(0)), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(s(0)))), timesIter(half(x0), x1, s(0))), TIMESITER(half(x0), x1, half(s(s(s(0))))), HALF(x0))
   IF(even, x0, x1, s(s(s(z0))), x3) -> c18(PLUS(timesIter(half(x0), x1, half(s(s(s(z0))))), timesIter(half(x0), x1, s(s(half(z0))))), TIMESITER(half(x0), x1, half(s(s(s(s(z0)))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c18(PLUS(timesIter(half(s(s(z0))), x1, half(s(x2))), timesIter(s(half(z0)), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, z1, s(x2), x3) -> c18(PLUS(if(check(half(x0)), half(x0), z1, half(s(x2)), plus(half(s(x2)), z1)), timesIter(half(x0), z1, s(half(x2)))), TIMESITER(half(x0), z1, half(s(s(x2)))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(timesIter(half(x0), x1, 0), timesIter(half(x0), x1, s(half(0)))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(x0), x1, s(half(z0))), timesIter(half(x0), x1, s(half(s(z0))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, s(x2), x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(s(x2))), timesIter(half(s(s(z0))), x1, s(half(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(s(x2)))), HALF(s(s(z0))))
   IF(even, x0, x1, s(x2), x3) -> c18(TIMESITER(half(x0), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(x2), x3) -> c18(PLUS(timesIter(half(0), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(x2), x3) -> c18(PLUS(timesIter(half(s(0)), x1, half(s(x2))), timesIter(0, x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, 0, x1, s(x2), x3) -> c18(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(0), x1, s(half(x2)))), TIMESITER(half(0), x1, half(s(s(x2)))))
   IF(even, s(0), x1, s(x2), x3) -> c18(PLUS(timesIter(0, x1, half(s(x2))), timesIter(half(s(0)), x1, s(half(x2)))), TIMESITER(half(s(0)), x1, half(s(s(x2)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c18(PLUS(timesIter(half(s(s(x0))), z1, half(x2)), if(check(s(half(x0))), s(half(x0)), z1, half(s(x2)), plus(half(s(x2)), z1))), TIMESITER(half(s(s(x0))), z1, half(s(x2))), HALF(s(s(x0))))
   IF(even, s(s(s(s(z0)))), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(s(s(z0))))), x1, half(x2)), timesIter(s(s(half(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(s(s(z0))))), x1, half(s(x2))), HALF(s(s(s(s(z0))))))
   IF(even, s(s(0)), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(0))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(0))), x1, half(s(x2))), HALF(s(s(0))))
   IF(even, s(s(s(0))), x1, x2, x3) -> c18(PLUS(timesIter(half(s(s(s(0)))), x1, half(x2)), timesIter(s(0), x1, half(s(x2)))), TIMESITER(half(s(s(s(0)))), x1, half(s(x2))), HALF(s(s(s(0)))))
   IF(even, s(s(x0)), z1, x2, x3) -> c18(PLUS(if(check(half(s(s(x0)))), half(s(s(x0))), z1, half(x2), plus(half(x2), z1)), timesIter(s(half(x0)), z1, half(s(x2)))), TIMESITER(half(s(s(x0))), z1, half(s(x2))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(s(z0)), x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, s(half(z0))), timesIter(s(half(x0)), x1, half(s(s(s(z0)))))), TIMESITER(half(s(s(x0))), x1, half(s(s(s(z0))))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, 0, x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(0)))), TIMESITER(half(s(s(x0))), x1, half(s(0))), HALF(s(s(x0))))
   IF(even, s(s(x0)), x1, s(0), x3) -> c18(PLUS(timesIter(half(s(s(x0))), x1, 0), timesIter(s(half(x0)), x1, half(s(s(0))))), TIMESITER(half(s(s(x0))), x1, half(s(s(0)))), HALF(s(s(x0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(timesIter(s(half(z0)), x1, half(x2)), timesIter(s(half(z0)), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, half(0), plus(0, x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, half(s(0)), plus(0, x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, half(s(s(z0))), plus(s(half(z0)), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, x0, x1, 0, x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(0), x1)), timesIter(half(x0), x1, half(s(0)))), TIMESITER(half(x0), x1, half(s(0))), HALF(x0))
   IF(even, x0, x1, s(0), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, 0, plus(half(s(0)), x1)), timesIter(half(x0), x1, half(s(s(0))))), TIMESITER(half(x0), x1, half(s(s(0)))), HALF(x0))
   IF(even, x0, x1, s(s(z0)), x3) -> c18(PLUS(if(check(half(x0)), half(x0), x1, s(half(z0)), plus(half(s(s(z0))), x1)), timesIter(half(x0), x1, half(s(s(s(z0)))))), TIMESITER(half(x0), x1, half(s(s(s(z0))))), HALF(x0))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(if(check(half(s(s(z0)))), s(half(z0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, s(s(z0)), x1, x2, x3) -> c18(PLUS(if(check(s(half(z0))), half(s(s(z0))), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(s(z0))), x1, half(s(x2)))), TIMESITER(half(s(s(z0))), x1, half(s(x2))), HALF(s(s(z0))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(if(check(half(0)), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(if(check(half(s(0))), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(0, x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(if(check(half(0)), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(if(check(half(s(0))), 0, x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, 0, x1, x2, x3) -> c18(PLUS(if(check(0), half(0), x1, half(x2), plus(half(x2), x1)), timesIter(half(0), x1, half(s(x2)))), TIMESITER(half(0), x1, half(s(x2))))
   IF(even, s(0), x1, x2, x3) -> c18(PLUS(if(check(0), half(s(0)), x1, half(x2), plus(half(x2), x1)), timesIter(half(s(0)), x1, half(s(x2)))), TIMESITER(half(s(0)), x1, half(s(x2))))
   IF(even, x0, z1, 0, x2) -> c18(PLUS(if(check(half(x0)), half(x0), z1, 0, plus(0, z1)), timesIter(half(x0), z1, half(s(0)))), TIMESITER(half(x0), z1, half(s(0))), HALF(x0))
   IF(even, s(s(z0)), x1, 0, x2) -> c18(PLUS(timesIter(s(half(z0)), x1, 0), timesIter(half(s(s(z0))), x1, half(s(0)))), TIMESITER(half(s(s(z0))), x1, half(s(0))), HALF(s(s(z0))))
K tuples:
   TIMESITER(0, x1, x2) -> c11(PLUS(x2, x1))
   TIMESITER(s(s(s(x0))), x1, x2) -> c10(CHECK(s(s(s(x0)))))
   TIMESITER(x0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   TIMESITER(0, x1, s(x2)) -> c11(PLUS(s(x2), x1))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c1(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c1(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c2(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c2(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c4(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c4(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c5(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c5(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c7(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c7(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, 0, x0, 0, x2) -> c9(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c9(PLUS(timesIter(half(0), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, half(0)), timesIter(0, x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c12(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c12(PLUS(timesIter(half(s(0)), x0, 0), timesIter(0, x0, half(s(0)))))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, half(0)), timesIter(half(0), x0, 0)))
   IF(even, 0, x0, 0, x2) -> c13(TIMESITER(half(0), x0, half(0)))
   IF(even, 0, x0, 0, x2) -> c13(PLUS(timesIter(0, x0, 0), timesIter(half(0), x0, half(s(0)))))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, half(0)), timesIter(half(s(0)), x0, 0)))
   IF(even, s(0), x0, 0, x2) -> c14(TIMESITER(half(s(0)), x0, half(0)))
   IF(even, s(0), x0, 0, x2) -> c14(PLUS(timesIter(0, x0, 0), timesIter(half(s(0)), x0, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c20(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c20(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c20(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c21(TIMESITER(half(0), x1, half(0)))
   IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c21(TIMESITER(half(s(0)), x1, half(0)))
   IF(even, 0, x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c21(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(half(0), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, 0, x1, 0, x2) -> c22(TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(half(s(0)), x1, half(0)), timesIter(0, x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c22(TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(0), x1, 0)))
   IF(even, s(0), x1, 0, x2) -> c22(PLUS(timesIter(0, x1, half(0)), timesIter(half(s(0)), x1, 0)))
   IF(even, 0, x1, 0, x2) -> c23(PLUS(timesIter(half(0), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, 0, x1, 0, x2) -> c23(TIMESITER(half(0), x1, half(s(0))))
   IF(even, s(0), x1, 0, x2) -> c23(PLUS(timesIter(half(s(0)), x1, 0), timesIter(0, x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c23(TIMESITER(half(s(0)), x1, half(s(0))))
   IF(even, 0, x1, 0, x2) -> c23(PLUS(timesIter(0, x1, 0), timesIter(half(0), x1, half(s(0)))))
   IF(even, s(0), x1, 0, x2) -> c23(PLUS(timesIter(0, x1, 0), timesIter(half(s(0)), x1, half(s(0)))))
Defined Rule Symbols:   check_1, plus_2, timesIter_3, half_1, if_5, p_1

Defined Pair Symbols:   CHECK_1, HALF_1, PLUS_2, IF_5, TIMESITER_3

Compound Symbols:   c3_1, c6_1, c8_1, c15_1, c10_1, c11_2, c11_1, c18_3, c18_2, c19_3, c19_2, c10_2, c16_3, c16_2, c_1, c1_1, c16_1, c2_1, c4_1, c5_1, c7_1, c17_3, c17_2, c9_1, c12_1, c13_1, c14_1, c20_1, c21_1, c17_1, c22_1, c18_1, c23_1