KILLED
proof of input_g1t8qhSLmR.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# AProVE Commit ID: aff8ecad908e01718a4c36e68d2e55d5e0f16e15 fuhs 20220216 unpublished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), 32 ms]
        (12) CpxTypedWeightedCompleteTrs
        (13) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 5 ms]
        (14) CpxRNTS
        (15) InliningProof [UPPER BOUND(ID), 690 ms]
        (16) CpxRNTS
        (17) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (18) CpxRNTS
    (19) CompletionProof [UPPER BOUND(ID), 0 ms]
    (20) CpxTypedWeightedCompleteTrs
        (21) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
        (22) CpxRNTS
(23) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms]
(24) CdtProblem
    (25) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (26) CdtProblem
    (27) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (28) CdtProblem
    (29) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (30) CdtProblem
    (31) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (32) CdtProblem
    (33) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (34) CdtProblem
    (35) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (36) CdtProblem
    (37) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (38) CdtProblem
    (39) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (40) CdtProblem
    (41) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (42) CdtProblem
    (43) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (44) CdtProblem
    (45) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (46) CdtProblem
    (47) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (48) CdtProblem
    (49) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (50) CdtProblem
    (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 29 ms]
    (52) CdtProblem
    (53) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (54) CdtProblem
    (55) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (56) CdtProblem
    (57) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (58) CdtProblem
    (59) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (60) CdtProblem
    (61) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (62) CdtProblem
    (63) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 78 ms]
    (64) CdtProblem
    (65) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (66) CdtProblem
    (67) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (68) CdtProblem
    (69) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 23 ms]
    (70) CdtProblem
    (71) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (72) CdtProblem
    (73) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 9 ms]
    (74) CdtProblem
    (75) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 83 ms]
    (76) CdtProblem
    (77) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (78) CdtProblem
    (79) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 5 ms]
    (80) CdtProblem
    (81) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 68 ms]
    (82) CdtProblem
    (83) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (84) CdtProblem
    (85) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (86) CdtProblem
    (87) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 118 ms]
    (88) CdtProblem
    (89) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (90) CdtProblem
    (91) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (92) CdtProblem
    (93) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (94) CdtProblem
    (95) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 12 ms]
    (96) CdtProblem
    (97) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (98) CdtProblem
    (99) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 80 ms]
    (100) CdtProblem
    (101) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (102) CdtProblem
    (103) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (104) CdtProblem
    (105) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 67 ms]
    (106) CdtProblem
    (107) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (108) CdtProblem
    (109) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (110) CdtProblem
    (111) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 39 ms]
    (112) CdtProblem
    (113) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (114) CdtProblem
    (115) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 47 ms]
    (116) CdtProblem
    (117) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (118) CdtProblem
    (119) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 170 ms]
    (120) CdtProblem
    (121) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 21 ms]
    (122) CdtProblem
    (123) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 100 ms]
    (124) CdtProblem
    (125) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (126) CdtProblem
    (127) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 89 ms]
    (128) CdtProblem
    (129) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 8 ms]
    (130) CdtProblem
    (131) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 81 ms]
    (132) CdtProblem
    (133) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 20 ms]
    (134) CdtProblem
    (135) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 42 ms]
    (136) CdtProblem
    (137) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (138) CdtProblem
    (139) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 290 ms]
    (140) CdtProblem
    (141) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 29 ms]
    (142) CdtProblem
    (143) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 79 ms]
    (144) CdtProblem
    (145) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (146) CdtProblem
    (147) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 173 ms]
    (148) CdtProblem
    (149) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 7 ms]
    (150) CdtProblem
    (151) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 124 ms]
    (152) CdtProblem
    (153) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 29 ms]
    (154) CdtProblem
    (155) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 132 ms]
    (156) CdtProblem
    (157) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (158) CdtProblem
    (159) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 232 ms]
    (160) CdtProblem
    (161) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 26 ms]
    (162) CdtProblem
    (163) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 276 ms]
    (164) CdtProblem
    (165) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 15 ms]
    (166) CdtProblem
    (167) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 354 ms]
    (168) CdtProblem
    (169) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 49 ms]
    (170) CdtProblem
    (171) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 312 ms]
    (172) CdtProblem
    (173) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 11 ms]
    (174) CdtProblem
    (175) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 517 ms]
    (176) CdtProblem
    (177) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 79 ms]
    (178) CdtProblem
    (179) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 157 ms]
    (180) CdtProblem
    (181) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 87 ms]
    (182) CdtProblem
    (183) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 169 ms]
    (184) CdtProblem
    (185) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 71 ms]
    (186) CdtProblem
    (187) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 135 ms]
    (188) CdtProblem
    (189) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 88 ms]
    (190) CdtProblem
    (191) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 473 ms]
    (192) CdtProblem
    (193) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 76 ms]
    (194) CdtProblem
    (195) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 69 ms]
    (196) CdtProblem
    (197) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 425 ms]
    (198) CdtProblem
    (199) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 119 ms]
    (200) CdtProblem
    (201) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 91 ms]
    (202) CdtProblem
    (203) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 573 ms]
    (204) CdtProblem
    (205) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 95 ms]
    (206) CdtProblem
    (207) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 76 ms]
    (208) CdtProblem
    (209) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 420 ms]
    (210) CdtProblem
    (211) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 151 ms]
    (212) CdtProblem
    (213) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 67 ms]
    (214) CdtProblem
    (215) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 717 ms]
    (216) CdtProblem
    (217) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 171 ms]
    (218) CdtProblem
    (219) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 147 ms]
    (220) CdtProblem
    (221) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 506 ms]
    (222) CdtProblem
    (223) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 161 ms]
    (224) CdtProblem
    (225) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 117 ms]
    (226) 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:

   a__terms(N) -> cons(recip(a__sqr(mark(N))), terms(s(N)))
   a__sqr(0) -> 0
   a__sqr(s(X)) -> s(add(sqr(X), dbl(X)))
   a__dbl(0) -> 0
   a__dbl(s(X)) -> s(s(dbl(X)))
   a__add(0, X) -> mark(X)
   a__add(s(X), Y) -> s(add(X, Y))
   a__first(0, X) -> nil
   a__first(s(X), cons(Y, Z)) -> cons(mark(Y), first(X, Z))
   mark(terms(X)) -> a__terms(mark(X))
   mark(sqr(X)) -> a__sqr(mark(X))
   mark(add(X1, X2)) -> a__add(mark(X1), mark(X2))
   mark(dbl(X)) -> a__dbl(mark(X))
   mark(first(X1, X2)) -> a__first(mark(X1), mark(X2))
   mark(cons(X1, X2)) -> cons(mark(X1), X2)
   mark(recip(X)) -> recip(mark(X))
   mark(s(X)) -> s(X)
   mark(0) -> 0
   mark(nil) -> nil
   a__terms(X) -> terms(X)
   a__sqr(X) -> sqr(X)
   a__add(X1, X2) -> add(X1, X2)
   a__dbl(X) -> dbl(X)
   a__first(X1, X2) -> first(X1, X2)

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:

   a__terms(N) -> cons(recip(a__sqr(mark(N))), terms(s(N)))
   a__sqr(0') -> 0'
   a__sqr(s(X)) -> s(add(sqr(X), dbl(X)))
   a__dbl(0') -> 0'
   a__dbl(s(X)) -> s(s(dbl(X)))
   a__add(0', X) -> mark(X)
   a__add(s(X), Y) -> s(add(X, Y))
   a__first(0', X) -> nil
   a__first(s(X), cons(Y, Z)) -> cons(mark(Y), first(X, Z))
   mark(terms(X)) -> a__terms(mark(X))
   mark(sqr(X)) -> a__sqr(mark(X))
   mark(add(X1, X2)) -> a__add(mark(X1), mark(X2))
   mark(dbl(X)) -> a__dbl(mark(X))
   mark(first(X1, X2)) -> a__first(mark(X1), mark(X2))
   mark(cons(X1, X2)) -> cons(mark(X1), X2)
   mark(recip(X)) -> recip(mark(X))
   mark(s(X)) -> s(X)
   mark(0') -> 0'
   mark(nil) -> nil
   a__terms(X) -> terms(X)
   a__sqr(X) -> sqr(X)
   a__add(X1, X2) -> add(X1, X2)
   a__dbl(X) -> dbl(X)
   a__first(X1, X2) -> first(X1, X2)

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:

   a__terms(N) -> cons(recip(a__sqr(mark(N))), terms(s(N)))
   a__sqr(0) -> 0
   a__sqr(s(X)) -> s(add(sqr(X), dbl(X)))
   a__dbl(0) -> 0
   a__dbl(s(X)) -> s(s(dbl(X)))
   a__add(0, X) -> mark(X)
   a__add(s(X), Y) -> s(add(X, Y))
   a__first(0, X) -> nil
   a__first(s(X), cons(Y, Z)) -> cons(mark(Y), first(X, Z))
   mark(terms(X)) -> a__terms(mark(X))
   mark(sqr(X)) -> a__sqr(mark(X))
   mark(add(X1, X2)) -> a__add(mark(X1), mark(X2))
   mark(dbl(X)) -> a__dbl(mark(X))
   mark(first(X1, X2)) -> a__first(mark(X1), mark(X2))
   mark(cons(X1, X2)) -> cons(mark(X1), X2)
   mark(recip(X)) -> recip(mark(X))
   mark(s(X)) -> s(X)
   mark(0) -> 0
   mark(nil) -> nil
   a__terms(X) -> terms(X)
   a__sqr(X) -> sqr(X)
   a__add(X1, X2) -> add(X1, X2)
   a__dbl(X) -> dbl(X)
   a__first(X1, X2) -> first(X1, X2)

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:

   a__terms(N) -> cons(recip(a__sqr(mark(N))), terms(s(N))) [1]
   a__sqr(0) -> 0 [1]
   a__sqr(s(X)) -> s(add(sqr(X), dbl(X))) [1]
   a__dbl(0) -> 0 [1]
   a__dbl(s(X)) -> s(s(dbl(X))) [1]
   a__add(0, X) -> mark(X) [1]
   a__add(s(X), Y) -> s(add(X, Y)) [1]
   a__first(0, X) -> nil [1]
   a__first(s(X), cons(Y, Z)) -> cons(mark(Y), first(X, Z)) [1]
   mark(terms(X)) -> a__terms(mark(X)) [1]
   mark(sqr(X)) -> a__sqr(mark(X)) [1]
   mark(add(X1, X2)) -> a__add(mark(X1), mark(X2)) [1]
   mark(dbl(X)) -> a__dbl(mark(X)) [1]
   mark(first(X1, X2)) -> a__first(mark(X1), mark(X2)) [1]
   mark(cons(X1, X2)) -> cons(mark(X1), X2) [1]
   mark(recip(X)) -> recip(mark(X)) [1]
   mark(s(X)) -> s(X) [1]
   mark(0) -> 0 [1]
   mark(nil) -> nil [1]
   a__terms(X) -> terms(X) [1]
   a__sqr(X) -> sqr(X) [1]
   a__add(X1, X2) -> add(X1, X2) [1]
   a__dbl(X) -> dbl(X) [1]
   a__first(X1, X2) -> first(X1, X2) [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:

   a__terms(N) -> cons(recip(a__sqr(mark(N))), terms(s(N))) [1]
   a__sqr(0) -> 0 [1]
   a__sqr(s(X)) -> s(add(sqr(X), dbl(X))) [1]
   a__dbl(0) -> 0 [1]
   a__dbl(s(X)) -> s(s(dbl(X))) [1]
   a__add(0, X) -> mark(X) [1]
   a__add(s(X), Y) -> s(add(X, Y)) [1]
   a__first(0, X) -> nil [1]
   a__first(s(X), cons(Y, Z)) -> cons(mark(Y), first(X, Z)) [1]
   mark(terms(X)) -> a__terms(mark(X)) [1]
   mark(sqr(X)) -> a__sqr(mark(X)) [1]
   mark(add(X1, X2)) -> a__add(mark(X1), mark(X2)) [1]
   mark(dbl(X)) -> a__dbl(mark(X)) [1]
   mark(first(X1, X2)) -> a__first(mark(X1), mark(X2)) [1]
   mark(cons(X1, X2)) -> cons(mark(X1), X2) [1]
   mark(recip(X)) -> recip(mark(X)) [1]
   mark(s(X)) -> s(X) [1]
   mark(0) -> 0 [1]
   mark(nil) -> nil [1]
   a__terms(X) -> terms(X) [1]
   a__sqr(X) -> sqr(X) [1]
   a__add(X1, X2) -> add(X1, X2) [1]
   a__dbl(X) -> dbl(X) [1]
   a__first(X1, X2) -> first(X1, X2) [1]

The TRS has the following type information:
a__terms :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first
cons :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first
recip :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first
a__sqr :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first
mark :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first
terms :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first
s :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first
0 :: recip:s:terms:cons:0:sqr:dbl:add:nil:first
add :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first
sqr :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first
dbl :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first
a__dbl :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first
a__add :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first
a__first :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first
nil :: recip:s:terms:cons:0:sqr:dbl:add:nil:first
first :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first

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:
none

(c) The following functions are completely defined:

   mark_1
   a__sqr_1
   a__add_2
   a__terms_1
   a__dbl_1
   a__first_2

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:

   a__terms(N) -> cons(recip(a__sqr(mark(N))), terms(s(N))) [1]
   a__sqr(0) -> 0 [1]
   a__sqr(s(X)) -> s(add(sqr(X), dbl(X))) [1]
   a__dbl(0) -> 0 [1]
   a__dbl(s(X)) -> s(s(dbl(X))) [1]
   a__add(0, X) -> mark(X) [1]
   a__add(s(X), Y) -> s(add(X, Y)) [1]
   a__first(0, X) -> nil [1]
   a__first(s(X), cons(Y, Z)) -> cons(mark(Y), first(X, Z)) [1]
   mark(terms(X)) -> a__terms(mark(X)) [1]
   mark(sqr(X)) -> a__sqr(mark(X)) [1]
   mark(add(X1, X2)) -> a__add(mark(X1), mark(X2)) [1]
   mark(dbl(X)) -> a__dbl(mark(X)) [1]
   mark(first(X1, X2)) -> a__first(mark(X1), mark(X2)) [1]
   mark(cons(X1, X2)) -> cons(mark(X1), X2) [1]
   mark(recip(X)) -> recip(mark(X)) [1]
   mark(s(X)) -> s(X) [1]
   mark(0) -> 0 [1]
   mark(nil) -> nil [1]
   a__terms(X) -> terms(X) [1]
   a__sqr(X) -> sqr(X) [1]
   a__add(X1, X2) -> add(X1, X2) [1]
   a__dbl(X) -> dbl(X) [1]
   a__first(X1, X2) -> first(X1, X2) [1]

The TRS has the following type information:
a__terms :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first
cons :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first
recip :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first
a__sqr :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first
mark :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first
terms :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first
s :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first
0 :: recip:s:terms:cons:0:sqr:dbl:add:nil:first
add :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first
sqr :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first
dbl :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first
a__dbl :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first
a__add :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first
a__first :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first
nil :: recip:s:terms:cons:0:sqr:dbl:add:nil:first
first :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first

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:

   a__terms(terms(X')) -> cons(recip(a__sqr(a__terms(mark(X')))), terms(s(terms(X')))) [2]
   a__terms(sqr(X'')) -> cons(recip(a__sqr(a__sqr(mark(X'')))), terms(s(sqr(X'')))) [2]
   a__terms(add(X1', X2')) -> cons(recip(a__sqr(a__add(mark(X1'), mark(X2')))), terms(s(add(X1', X2')))) [2]
   a__terms(dbl(X3)) -> cons(recip(a__sqr(a__dbl(mark(X3)))), terms(s(dbl(X3)))) [2]
   a__terms(first(X1'', X2'')) -> cons(recip(a__sqr(a__first(mark(X1''), mark(X2'')))), terms(s(first(X1'', X2'')))) [2]
   a__terms(cons(X11, X21)) -> cons(recip(a__sqr(cons(mark(X11), X21))), terms(s(cons(X11, X21)))) [2]
   a__terms(recip(X4)) -> cons(recip(a__sqr(recip(mark(X4)))), terms(s(recip(X4)))) [2]
   a__terms(s(X5)) -> cons(recip(a__sqr(s(X5))), terms(s(s(X5)))) [2]
   a__terms(0) -> cons(recip(a__sqr(0)), terms(s(0))) [2]
   a__terms(nil) -> cons(recip(a__sqr(nil)), terms(s(nil))) [2]
   a__sqr(0) -> 0 [1]
   a__sqr(s(X)) -> s(add(sqr(X), dbl(X))) [1]
   a__dbl(0) -> 0 [1]
   a__dbl(s(X)) -> s(s(dbl(X))) [1]
   a__add(0, X) -> mark(X) [1]
   a__add(s(X), Y) -> s(add(X, Y)) [1]
   a__first(0, X) -> nil [1]
   a__first(s(X), cons(Y, Z)) -> cons(mark(Y), first(X, Z)) [1]
   mark(terms(terms(X6))) -> a__terms(a__terms(mark(X6))) [2]
   mark(terms(sqr(X7))) -> a__terms(a__sqr(mark(X7))) [2]
   mark(terms(add(X12, X22))) -> a__terms(a__add(mark(X12), mark(X22))) [2]
   mark(terms(dbl(X8))) -> a__terms(a__dbl(mark(X8))) [2]
   mark(terms(first(X13, X23))) -> a__terms(a__first(mark(X13), mark(X23))) [2]
   mark(terms(cons(X14, X24))) -> a__terms(cons(mark(X14), X24)) [2]
   mark(terms(recip(X9))) -> a__terms(recip(mark(X9))) [2]
   mark(terms(s(X10))) -> a__terms(s(X10)) [2]
   mark(terms(0)) -> a__terms(0) [2]
   mark(terms(nil)) -> a__terms(nil) [2]
   mark(sqr(terms(X15))) -> a__sqr(a__terms(mark(X15))) [2]
   mark(sqr(sqr(X16))) -> a__sqr(a__sqr(mark(X16))) [2]
   mark(sqr(add(X17, X25))) -> a__sqr(a__add(mark(X17), mark(X25))) [2]
   mark(sqr(dbl(X18))) -> a__sqr(a__dbl(mark(X18))) [2]
   mark(sqr(first(X19, X26))) -> a__sqr(a__first(mark(X19), mark(X26))) [2]
   mark(sqr(cons(X110, X27))) -> a__sqr(cons(mark(X110), X27)) [2]
   mark(sqr(recip(X20))) -> a__sqr(recip(mark(X20))) [2]
   mark(sqr(s(X28))) -> a__sqr(s(X28)) [2]
   mark(sqr(0)) -> a__sqr(0) [2]
   mark(sqr(nil)) -> a__sqr(nil) [2]
   mark(add(X1, X2)) -> a__add(mark(X1), mark(X2)) [1]
   mark(dbl(terms(X84))) -> a__dbl(a__terms(mark(X84))) [2]
   mark(dbl(sqr(X85))) -> a__dbl(a__sqr(mark(X85))) [2]
   mark(dbl(add(X144, X243))) -> a__dbl(a__add(mark(X144), mark(X243))) [2]
   mark(dbl(dbl(X86))) -> a__dbl(a__dbl(mark(X86))) [2]
   mark(dbl(first(X145, X244))) -> a__dbl(a__first(mark(X145), mark(X244))) [2]
   mark(dbl(cons(X146, X245))) -> a__dbl(cons(mark(X146), X245)) [2]
   mark(dbl(recip(X87))) -> a__dbl(recip(mark(X87))) [2]
   mark(dbl(s(X88))) -> a__dbl(s(X88)) [2]
   mark(dbl(0)) -> a__dbl(0) [2]
   mark(dbl(nil)) -> a__dbl(nil) [2]
   mark(first(X1, X2)) -> a__first(mark(X1), mark(X2)) [1]
   mark(cons(X1, X2)) -> cons(mark(X1), X2) [1]
   mark(recip(X)) -> recip(mark(X)) [1]
   mark(s(X)) -> s(X) [1]
   mark(0) -> 0 [1]
   mark(nil) -> nil [1]
   a__terms(X) -> terms(X) [1]
   a__sqr(X) -> sqr(X) [1]
   a__add(X1, X2) -> add(X1, X2) [1]
   a__dbl(X) -> dbl(X) [1]
   a__first(X1, X2) -> first(X1, X2) [1]

The TRS has the following type information:
a__terms :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first
cons :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first
recip :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first
a__sqr :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first
mark :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first
terms :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first
s :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first
0 :: recip:s:terms:cons:0:sqr:dbl:add:nil:first
add :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first
sqr :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first
dbl :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first
a__dbl :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first
a__add :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first
a__first :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first
nil :: recip:s:terms:cons:0:sqr:dbl:add:nil:first
first :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first

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
   nil => 1

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

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

   a__add(z, z') -{ 1 }-> mark(X) :|: z' = X, X >= 0, z = 0
   a__add(z, z') -{ 1 }-> 1 + (1 + X + Y) :|: z = 1 + X, z' = Y, Y >= 0, X >= 0
   a__add(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2
   a__dbl(z) -{ 1 }-> 0 :|: z = 0
   a__dbl(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__dbl(z) -{ 1 }-> 1 + (1 + (1 + X)) :|: z = 1 + X, X >= 0
   a__first(z, z') -{ 1 }-> 1 :|: z' = X, X >= 0, z = 0
   a__first(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2
   a__first(z, z') -{ 1 }-> 1 + mark(Y) + (1 + X + Z) :|: Z >= 0, z = 1 + X, Y >= 0, X >= 0, z' = 1 + Y + Z
   a__sqr(z) -{ 1 }-> 0 :|: z = 0
   a__sqr(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__sqr(z) -{ 1 }-> 1 + (1 + (1 + X) + (1 + X)) :|: z = 1 + X, X >= 0
   a__terms(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__terms(z) -{ 2 }-> 1 + (1 + a__sqr(a__terms(mark(X')))) + (1 + (1 + (1 + X'))) :|: X' >= 0, z = 1 + X'
   a__terms(z) -{ 2 }-> 1 + (1 + a__sqr(a__sqr(mark(X'')))) + (1 + (1 + (1 + X''))) :|: z = 1 + X'', X'' >= 0
   a__terms(z) -{ 2 }-> 1 + (1 + a__sqr(a__first(mark(X1''), mark(X2'')))) + (1 + (1 + (1 + X1'' + X2''))) :|: X1'' >= 0, z = 1 + X1'' + X2'', X2'' >= 0
   a__terms(z) -{ 2 }-> 1 + (1 + a__sqr(a__dbl(mark(X3)))) + (1 + (1 + (1 + X3))) :|: z = 1 + X3, X3 >= 0
   a__terms(z) -{ 2 }-> 1 + (1 + a__sqr(a__add(mark(X1'), mark(X2')))) + (1 + (1 + (1 + X1' + X2'))) :|: X2' >= 0, X1' >= 0, z = 1 + X1' + X2'
   a__terms(z) -{ 2 }-> 1 + (1 + a__sqr(1)) + (1 + (1 + 1)) :|: z = 1
   a__terms(z) -{ 2 }-> 1 + (1 + a__sqr(0)) + (1 + (1 + 0)) :|: z = 0
   a__terms(z) -{ 2 }-> 1 + (1 + a__sqr(1 + X5)) + (1 + (1 + (1 + X5))) :|: X5 >= 0, z = 1 + X5
   a__terms(z) -{ 2 }-> 1 + (1 + a__sqr(1 + mark(X4))) + (1 + (1 + (1 + X4))) :|: z = 1 + X4, X4 >= 0
   a__terms(z) -{ 2 }-> 1 + (1 + a__sqr(1 + mark(X11) + X21)) + (1 + (1 + (1 + X11 + X21))) :|: X11 >= 0, X21 >= 0, z = 1 + X11 + X21
   mark(z) -{ 2 }-> a__terms(a__terms(mark(X6))) :|: X6 >= 0, z = 1 + (1 + X6)
   mark(z) -{ 2 }-> a__terms(a__sqr(mark(X7))) :|: X7 >= 0, z = 1 + (1 + X7)
   mark(z) -{ 2 }-> a__terms(a__first(mark(X13), mark(X23))) :|: z = 1 + (1 + X13 + X23), X13 >= 0, X23 >= 0
   mark(z) -{ 2 }-> a__terms(a__dbl(mark(X8))) :|: X8 >= 0, z = 1 + (1 + X8)
   mark(z) -{ 2 }-> a__terms(a__add(mark(X12), mark(X22))) :|: X12 >= 0, X22 >= 0, z = 1 + (1 + X12 + X22)
   mark(z) -{ 2 }-> a__terms(1) :|: z = 1 + 1
   mark(z) -{ 2 }-> a__terms(0) :|: z = 1 + 0
   mark(z) -{ 2 }-> a__terms(1 + X10) :|: z = 1 + (1 + X10), X10 >= 0
   mark(z) -{ 2 }-> a__terms(1 + mark(X9)) :|: X9 >= 0, z = 1 + (1 + X9)
   mark(z) -{ 2 }-> a__terms(1 + mark(X14) + X24) :|: z = 1 + (1 + X14 + X24), X14 >= 0, X24 >= 0
   mark(z) -{ 2 }-> a__sqr(a__terms(mark(X15))) :|: z = 1 + (1 + X15), X15 >= 0
   mark(z) -{ 2 }-> a__sqr(a__sqr(mark(X16))) :|: X16 >= 0, z = 1 + (1 + X16)
   mark(z) -{ 2 }-> a__sqr(a__first(mark(X19), mark(X26))) :|: z = 1 + (1 + X19 + X26), X26 >= 0, X19 >= 0
   mark(z) -{ 2 }-> a__sqr(a__dbl(mark(X18))) :|: X18 >= 0, z = 1 + (1 + X18)
   mark(z) -{ 2 }-> a__sqr(a__add(mark(X17), mark(X25))) :|: X17 >= 0, z = 1 + (1 + X17 + X25), X25 >= 0
   mark(z) -{ 2 }-> a__sqr(1) :|: z = 1 + 1
   mark(z) -{ 2 }-> a__sqr(0) :|: z = 1 + 0
   mark(z) -{ 2 }-> a__sqr(1 + X28) :|: X28 >= 0, z = 1 + (1 + X28)
   mark(z) -{ 2 }-> a__sqr(1 + mark(X20)) :|: z = 1 + (1 + X20), X20 >= 0
   mark(z) -{ 2 }-> a__sqr(1 + mark(X110) + X27) :|: X110 >= 0, X27 >= 0, z = 1 + (1 + X110 + X27)
   mark(z) -{ 1 }-> a__first(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   mark(z) -{ 2 }-> a__dbl(a__terms(mark(X84))) :|: z = 1 + (1 + X84), X84 >= 0
   mark(z) -{ 2 }-> a__dbl(a__sqr(mark(X85))) :|: z = 1 + (1 + X85), X85 >= 0
   mark(z) -{ 2 }-> a__dbl(a__first(mark(X145), mark(X244))) :|: X244 >= 0, z = 1 + (1 + X145 + X244), X145 >= 0
   mark(z) -{ 2 }-> a__dbl(a__dbl(mark(X86))) :|: z = 1 + (1 + X86), X86 >= 0
   mark(z) -{ 2 }-> a__dbl(a__add(mark(X144), mark(X243))) :|: X243 >= 0, X144 >= 0, z = 1 + (1 + X144 + X243)
   mark(z) -{ 2 }-> a__dbl(1) :|: z = 1 + 1
   mark(z) -{ 2 }-> a__dbl(0) :|: z = 1 + 0
   mark(z) -{ 2 }-> a__dbl(1 + X88) :|: X88 >= 0, z = 1 + (1 + X88)
   mark(z) -{ 2 }-> a__dbl(1 + mark(X87)) :|: X87 >= 0, z = 1 + (1 + X87)
   mark(z) -{ 2 }-> a__dbl(1 + mark(X146) + X245) :|: X146 >= 0, X245 >= 0, z = 1 + (1 + X146 + X245)
   mark(z) -{ 1 }-> a__add(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   mark(z) -{ 1 }-> 1 :|: z = 1
   mark(z) -{ 1 }-> 0 :|: z = 0
   mark(z) -{ 1 }-> 1 + X :|: z = 1 + X, X >= 0
   mark(z) -{ 1 }-> 1 + mark(X) :|: z = 1 + X, X >= 0
   mark(z) -{ 1 }-> 1 + mark(X1) + X2 :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2


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

(15) InliningProof (UPPER BOUND(ID))
Inlined the following terminating rules on right-hand sides where appropriate:

   a__sqr(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__sqr(z) -{ 1 }-> 1 + (1 + (1 + X) + (1 + X)) :|: z = 1 + X, X >= 0
   a__sqr(z) -{ 1 }-> 0 :|: z = 0
   a__dbl(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__dbl(z) -{ 1 }-> 1 + (1 + (1 + X)) :|: z = 1 + X, X >= 0
   a__dbl(z) -{ 1 }-> 0 :|: z = 0

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

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

   a__add(z, z') -{ 1 }-> mark(X) :|: z' = X, X >= 0, z = 0
   a__add(z, z') -{ 1 }-> 1 + (1 + X + Y) :|: z = 1 + X, z' = Y, Y >= 0, X >= 0
   a__add(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2
   a__dbl(z) -{ 1 }-> 0 :|: z = 0
   a__dbl(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__dbl(z) -{ 1 }-> 1 + (1 + (1 + X)) :|: z = 1 + X, X >= 0
   a__first(z, z') -{ 1 }-> 1 :|: z' = X, X >= 0, z = 0
   a__first(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2
   a__first(z, z') -{ 1 }-> 1 + mark(Y) + (1 + X + Z) :|: Z >= 0, z = 1 + X, Y >= 0, X >= 0, z' = 1 + Y + Z
   a__sqr(z) -{ 1 }-> 0 :|: z = 0
   a__sqr(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__sqr(z) -{ 1 }-> 1 + (1 + (1 + X) + (1 + X)) :|: z = 1 + X, X >= 0
   a__terms(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__terms(z) -{ 2 }-> 1 + (1 + a__sqr(a__terms(mark(X')))) + (1 + (1 + (1 + X'))) :|: X' >= 0, z = 1 + X'
   a__terms(z) -{ 2 }-> 1 + (1 + a__sqr(a__sqr(mark(X'')))) + (1 + (1 + (1 + X''))) :|: z = 1 + X'', X'' >= 0
   a__terms(z) -{ 2 }-> 1 + (1 + a__sqr(a__first(mark(X1''), mark(X2'')))) + (1 + (1 + (1 + X1'' + X2''))) :|: X1'' >= 0, z = 1 + X1'' + X2'', X2'' >= 0
   a__terms(z) -{ 2 }-> 1 + (1 + a__sqr(a__dbl(mark(X3)))) + (1 + (1 + (1 + X3))) :|: z = 1 + X3, X3 >= 0
   a__terms(z) -{ 2 }-> 1 + (1 + a__sqr(a__add(mark(X1'), mark(X2')))) + (1 + (1 + (1 + X1' + X2'))) :|: X2' >= 0, X1' >= 0, z = 1 + X1' + X2'
   a__terms(z) -{ 2 }-> 1 + (1 + a__sqr(1 + mark(X4))) + (1 + (1 + (1 + X4))) :|: z = 1 + X4, X4 >= 0
   a__terms(z) -{ 2 }-> 1 + (1 + a__sqr(1 + mark(X11) + X21)) + (1 + (1 + (1 + X11 + X21))) :|: X11 >= 0, X21 >= 0, z = 1 + X11 + X21
   a__terms(z) -{ 3 }-> 1 + (1 + 0) + (1 + (1 + 0)) :|: z = 0, 0 = 0
   a__terms(z) -{ 3 }-> 1 + (1 + (1 + X)) + (1 + (1 + 1)) :|: z = 1, X >= 0, 1 = X
   a__terms(z) -{ 3 }-> 1 + (1 + (1 + X)) + (1 + (1 + 0)) :|: z = 0, X >= 0, 0 = X
   a__terms(z) -{ 3 }-> 1 + (1 + (1 + X)) + (1 + (1 + (1 + X5))) :|: X5 >= 0, z = 1 + X5, X >= 0, 1 + X5 = X
   a__terms(z) -{ 3 }-> 1 + (1 + (1 + (1 + (1 + X) + (1 + X)))) + (1 + (1 + 1)) :|: z = 1, 1 = 1 + X, X >= 0
   a__terms(z) -{ 3 }-> 1 + (1 + (1 + (1 + (1 + X) + (1 + X)))) + (1 + (1 + (1 + X5))) :|: X5 >= 0, z = 1 + X5, 1 + X5 = 1 + X, X >= 0
   mark(z) -{ 2 }-> a__terms(a__terms(mark(X6))) :|: X6 >= 0, z = 1 + (1 + X6)
   mark(z) -{ 2 }-> a__terms(a__sqr(mark(X7))) :|: X7 >= 0, z = 1 + (1 + X7)
   mark(z) -{ 2 }-> a__terms(a__first(mark(X13), mark(X23))) :|: z = 1 + (1 + X13 + X23), X13 >= 0, X23 >= 0
   mark(z) -{ 2 }-> a__terms(a__dbl(mark(X8))) :|: X8 >= 0, z = 1 + (1 + X8)
   mark(z) -{ 2 }-> a__terms(a__add(mark(X12), mark(X22))) :|: X12 >= 0, X22 >= 0, z = 1 + (1 + X12 + X22)
   mark(z) -{ 2 }-> a__terms(1) :|: z = 1 + 1
   mark(z) -{ 2 }-> a__terms(0) :|: z = 1 + 0
   mark(z) -{ 2 }-> a__terms(1 + X10) :|: z = 1 + (1 + X10), X10 >= 0
   mark(z) -{ 2 }-> a__terms(1 + mark(X9)) :|: X9 >= 0, z = 1 + (1 + X9)
   mark(z) -{ 2 }-> a__terms(1 + mark(X14) + X24) :|: z = 1 + (1 + X14 + X24), X14 >= 0, X24 >= 0
   mark(z) -{ 2 }-> a__sqr(a__terms(mark(X15))) :|: z = 1 + (1 + X15), X15 >= 0
   mark(z) -{ 2 }-> a__sqr(a__sqr(mark(X16))) :|: X16 >= 0, z = 1 + (1 + X16)
   mark(z) -{ 2 }-> a__sqr(a__first(mark(X19), mark(X26))) :|: z = 1 + (1 + X19 + X26), X26 >= 0, X19 >= 0
   mark(z) -{ 2 }-> a__sqr(a__dbl(mark(X18))) :|: X18 >= 0, z = 1 + (1 + X18)
   mark(z) -{ 2 }-> a__sqr(a__add(mark(X17), mark(X25))) :|: X17 >= 0, z = 1 + (1 + X17 + X25), X25 >= 0
   mark(z) -{ 2 }-> a__sqr(1 + mark(X20)) :|: z = 1 + (1 + X20), X20 >= 0
   mark(z) -{ 2 }-> a__sqr(1 + mark(X110) + X27) :|: X110 >= 0, X27 >= 0, z = 1 + (1 + X110 + X27)
   mark(z) -{ 1 }-> a__first(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   mark(z) -{ 2 }-> a__dbl(a__terms(mark(X84))) :|: z = 1 + (1 + X84), X84 >= 0
   mark(z) -{ 2 }-> a__dbl(a__sqr(mark(X85))) :|: z = 1 + (1 + X85), X85 >= 0
   mark(z) -{ 2 }-> a__dbl(a__first(mark(X145), mark(X244))) :|: X244 >= 0, z = 1 + (1 + X145 + X244), X145 >= 0
   mark(z) -{ 2 }-> a__dbl(a__dbl(mark(X86))) :|: z = 1 + (1 + X86), X86 >= 0
   mark(z) -{ 2 }-> a__dbl(a__add(mark(X144), mark(X243))) :|: X243 >= 0, X144 >= 0, z = 1 + (1 + X144 + X243)
   mark(z) -{ 2 }-> a__dbl(1 + mark(X87)) :|: X87 >= 0, z = 1 + (1 + X87)
   mark(z) -{ 2 }-> a__dbl(1 + mark(X146) + X245) :|: X146 >= 0, X245 >= 0, z = 1 + (1 + X146 + X245)
   mark(z) -{ 1 }-> a__add(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   mark(z) -{ 1 }-> 1 :|: z = 1
   mark(z) -{ 1 }-> 0 :|: z = 0
   mark(z) -{ 3 }-> 0 :|: z = 1 + 0, 0 = 0
   mark(z) -{ 1 }-> 1 + X :|: z = 1 + X, X >= 0
   mark(z) -{ 3 }-> 1 + X :|: X28 >= 0, z = 1 + (1 + X28), X >= 0, 1 + X28 = X
   mark(z) -{ 3 }-> 1 + X :|: z = 1 + 0, X >= 0, 0 = X
   mark(z) -{ 3 }-> 1 + X :|: z = 1 + 1, X >= 0, 1 = X
   mark(z) -{ 3 }-> 1 + X :|: X88 >= 0, z = 1 + (1 + X88), X >= 0, 1 + X88 = X
   mark(z) -{ 1 }-> 1 + mark(X) :|: z = 1 + X, X >= 0
   mark(z) -{ 3 }-> 1 + (1 + (1 + X)) :|: X88 >= 0, z = 1 + (1 + X88), 1 + X88 = 1 + X, X >= 0
   mark(z) -{ 3 }-> 1 + (1 + (1 + X)) :|: z = 1 + 1, 1 = 1 + X, X >= 0
   mark(z) -{ 3 }-> 1 + (1 + (1 + X) + (1 + X)) :|: X28 >= 0, z = 1 + (1 + X28), 1 + X28 = 1 + X, X >= 0
   mark(z) -{ 3 }-> 1 + (1 + (1 + X) + (1 + X)) :|: z = 1 + 1, 1 = 1 + X, X >= 0
   mark(z) -{ 1 }-> 1 + mark(X1) + X2 :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2


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

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

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

   a__add(z, z') -{ 1 }-> mark(z') :|: z' >= 0, z = 0
   a__add(z, z') -{ 1 }-> 1 + (1 + (z - 1) + z') :|: z' >= 0, z - 1 >= 0
   a__add(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0
   a__dbl(z) -{ 1 }-> 0 :|: z = 0
   a__dbl(z) -{ 1 }-> 1 + z :|: z >= 0
   a__dbl(z) -{ 1 }-> 1 + (1 + (1 + (z - 1))) :|: z - 1 >= 0
   a__first(z, z') -{ 1 }-> 1 :|: z' >= 0, z = 0
   a__first(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0
   a__first(z, z') -{ 1 }-> 1 + mark(Y) + (1 + (z - 1) + Z) :|: Z >= 0, Y >= 0, z - 1 >= 0, z' = 1 + Y + Z
   a__sqr(z) -{ 1 }-> 0 :|: z = 0
   a__sqr(z) -{ 1 }-> 1 + z :|: z >= 0
   a__sqr(z) -{ 1 }-> 1 + (1 + (1 + (z - 1)) + (1 + (z - 1))) :|: z - 1 >= 0
   a__terms(z) -{ 1 }-> 1 + z :|: z >= 0
   a__terms(z) -{ 2 }-> 1 + (1 + a__sqr(a__terms(mark(z - 1)))) + (1 + (1 + (1 + (z - 1)))) :|: z - 1 >= 0
   a__terms(z) -{ 2 }-> 1 + (1 + a__sqr(a__sqr(mark(z - 1)))) + (1 + (1 + (1 + (z - 1)))) :|: z - 1 >= 0
   a__terms(z) -{ 2 }-> 1 + (1 + a__sqr(a__first(mark(X1''), mark(X2'')))) + (1 + (1 + (1 + X1'' + X2''))) :|: X1'' >= 0, z = 1 + X1'' + X2'', X2'' >= 0
   a__terms(z) -{ 2 }-> 1 + (1 + a__sqr(a__dbl(mark(z - 1)))) + (1 + (1 + (1 + (z - 1)))) :|: z - 1 >= 0
   a__terms(z) -{ 2 }-> 1 + (1 + a__sqr(a__add(mark(X1'), mark(X2')))) + (1 + (1 + (1 + X1' + X2'))) :|: X2' >= 0, X1' >= 0, z = 1 + X1' + X2'
   a__terms(z) -{ 2 }-> 1 + (1 + a__sqr(1 + mark(z - 1))) + (1 + (1 + (1 + (z - 1)))) :|: z - 1 >= 0
   a__terms(z) -{ 2 }-> 1 + (1 + a__sqr(1 + mark(X11) + X21)) + (1 + (1 + (1 + X11 + X21))) :|: X11 >= 0, X21 >= 0, z = 1 + X11 + X21
   a__terms(z) -{ 3 }-> 1 + (1 + 0) + (1 + (1 + 0)) :|: z = 0, 0 = 0
   a__terms(z) -{ 3 }-> 1 + (1 + (1 + X)) + (1 + (1 + 1)) :|: z = 1, X >= 0, 1 = X
   a__terms(z) -{ 3 }-> 1 + (1 + (1 + X)) + (1 + (1 + 0)) :|: z = 0, X >= 0, 0 = X
   a__terms(z) -{ 3 }-> 1 + (1 + (1 + X)) + (1 + (1 + (1 + (z - 1)))) :|: z - 1 >= 0, X >= 0, 1 + (z - 1) = X
   a__terms(z) -{ 3 }-> 1 + (1 + (1 + (1 + (1 + X) + (1 + X)))) + (1 + (1 + 1)) :|: z = 1, 1 = 1 + X, X >= 0
   a__terms(z) -{ 3 }-> 1 + (1 + (1 + (1 + (1 + X) + (1 + X)))) + (1 + (1 + (1 + (z - 1)))) :|: z - 1 >= 0, 1 + (z - 1) = 1 + X, X >= 0
   mark(z) -{ 2 }-> a__terms(a__terms(mark(z - 2))) :|: z - 2 >= 0
   mark(z) -{ 2 }-> a__terms(a__sqr(mark(z - 2))) :|: z - 2 >= 0
   mark(z) -{ 2 }-> a__terms(a__first(mark(X13), mark(X23))) :|: z = 1 + (1 + X13 + X23), X13 >= 0, X23 >= 0
   mark(z) -{ 2 }-> a__terms(a__dbl(mark(z - 2))) :|: z - 2 >= 0
   mark(z) -{ 2 }-> a__terms(a__add(mark(X12), mark(X22))) :|: X12 >= 0, X22 >= 0, z = 1 + (1 + X12 + X22)
   mark(z) -{ 2 }-> a__terms(1) :|: z = 1 + 1
   mark(z) -{ 2 }-> a__terms(0) :|: z = 1 + 0
   mark(z) -{ 2 }-> a__terms(1 + mark(z - 2)) :|: z - 2 >= 0
   mark(z) -{ 2 }-> a__terms(1 + (z - 2)) :|: z - 2 >= 0
   mark(z) -{ 2 }-> a__terms(1 + mark(X14) + X24) :|: z = 1 + (1 + X14 + X24), X14 >= 0, X24 >= 0
   mark(z) -{ 2 }-> a__sqr(a__terms(mark(z - 2))) :|: z - 2 >= 0
   mark(z) -{ 2 }-> a__sqr(a__sqr(mark(z - 2))) :|: z - 2 >= 0
   mark(z) -{ 2 }-> a__sqr(a__first(mark(X19), mark(X26))) :|: z = 1 + (1 + X19 + X26), X26 >= 0, X19 >= 0
   mark(z) -{ 2 }-> a__sqr(a__dbl(mark(z - 2))) :|: z - 2 >= 0
   mark(z) -{ 2 }-> a__sqr(a__add(mark(X17), mark(X25))) :|: X17 >= 0, z = 1 + (1 + X17 + X25), X25 >= 0
   mark(z) -{ 2 }-> a__sqr(1 + mark(z - 2)) :|: z - 2 >= 0
   mark(z) -{ 2 }-> a__sqr(1 + mark(X110) + X27) :|: X110 >= 0, X27 >= 0, z = 1 + (1 + X110 + X27)
   mark(z) -{ 1 }-> a__first(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   mark(z) -{ 2 }-> a__dbl(a__terms(mark(z - 2))) :|: z - 2 >= 0
   mark(z) -{ 2 }-> a__dbl(a__sqr(mark(z - 2))) :|: z - 2 >= 0
   mark(z) -{ 2 }-> a__dbl(a__first(mark(X145), mark(X244))) :|: X244 >= 0, z = 1 + (1 + X145 + X244), X145 >= 0
   mark(z) -{ 2 }-> a__dbl(a__dbl(mark(z - 2))) :|: z - 2 >= 0
   mark(z) -{ 2 }-> a__dbl(a__add(mark(X144), mark(X243))) :|: X243 >= 0, X144 >= 0, z = 1 + (1 + X144 + X243)
   mark(z) -{ 2 }-> a__dbl(1 + mark(z - 2)) :|: z - 2 >= 0
   mark(z) -{ 2 }-> a__dbl(1 + mark(X146) + X245) :|: X146 >= 0, X245 >= 0, z = 1 + (1 + X146 + X245)
   mark(z) -{ 1 }-> a__add(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   mark(z) -{ 1 }-> 1 :|: z = 1
   mark(z) -{ 1 }-> 0 :|: z = 0
   mark(z) -{ 3 }-> 0 :|: z = 1 + 0, 0 = 0
   mark(z) -{ 3 }-> 1 + X :|: z - 2 >= 0, X >= 0, 1 + (z - 2) = X
   mark(z) -{ 3 }-> 1 + X :|: z = 1 + 0, X >= 0, 0 = X
   mark(z) -{ 3 }-> 1 + X :|: z = 1 + 1, X >= 0, 1 = X
   mark(z) -{ 1 }-> 1 + mark(z - 1) :|: z - 1 >= 0
   mark(z) -{ 1 }-> 1 + (z - 1) :|: z - 1 >= 0
   mark(z) -{ 3 }-> 1 + (1 + (1 + X)) :|: z - 2 >= 0, 1 + (z - 2) = 1 + X, X >= 0
   mark(z) -{ 3 }-> 1 + (1 + (1 + X)) :|: z = 1 + 1, 1 = 1 + X, X >= 0
   mark(z) -{ 3 }-> 1 + (1 + (1 + X) + (1 + X)) :|: z - 2 >= 0, 1 + (z - 2) = 1 + X, X >= 0
   mark(z) -{ 3 }-> 1 + (1 + (1 + X) + (1 + X)) :|: z = 1 + 1, 1 = 1 + X, X >= 0
   mark(z) -{ 1 }-> 1 + mark(X1) + X2 :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2


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

(19) 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

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

(20)
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:

   a__terms(N) -> cons(recip(a__sqr(mark(N))), terms(s(N))) [1]
   a__sqr(0) -> 0 [1]
   a__sqr(s(X)) -> s(add(sqr(X), dbl(X))) [1]
   a__dbl(0) -> 0 [1]
   a__dbl(s(X)) -> s(s(dbl(X))) [1]
   a__add(0, X) -> mark(X) [1]
   a__add(s(X), Y) -> s(add(X, Y)) [1]
   a__first(0, X) -> nil [1]
   a__first(s(X), cons(Y, Z)) -> cons(mark(Y), first(X, Z)) [1]
   mark(terms(X)) -> a__terms(mark(X)) [1]
   mark(sqr(X)) -> a__sqr(mark(X)) [1]
   mark(add(X1, X2)) -> a__add(mark(X1), mark(X2)) [1]
   mark(dbl(X)) -> a__dbl(mark(X)) [1]
   mark(first(X1, X2)) -> a__first(mark(X1), mark(X2)) [1]
   mark(cons(X1, X2)) -> cons(mark(X1), X2) [1]
   mark(recip(X)) -> recip(mark(X)) [1]
   mark(s(X)) -> s(X) [1]
   mark(0) -> 0 [1]
   mark(nil) -> nil [1]
   a__terms(X) -> terms(X) [1]
   a__sqr(X) -> sqr(X) [1]
   a__add(X1, X2) -> add(X1, X2) [1]
   a__dbl(X) -> dbl(X) [1]
   a__first(X1, X2) -> first(X1, X2) [1]

The TRS has the following type information:
a__terms :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first
cons :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first
recip :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first
a__sqr :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first
mark :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first
terms :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first
s :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first
0 :: recip:s:terms:cons:0:sqr:dbl:add:nil:first
add :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first
sqr :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first
dbl :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first
a__dbl :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first
a__add :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first
a__first :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first
nil :: recip:s:terms:cons:0:sqr:dbl:add:nil:first
first :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first

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

(21) 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
   nil => 1

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

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

   a__add(z, z') -{ 1 }-> mark(X) :|: z' = X, X >= 0, z = 0
   a__add(z, z') -{ 1 }-> 1 + (1 + X + Y) :|: z = 1 + X, z' = Y, Y >= 0, X >= 0
   a__add(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2
   a__dbl(z) -{ 1 }-> 0 :|: z = 0
   a__dbl(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__dbl(z) -{ 1 }-> 1 + (1 + (1 + X)) :|: z = 1 + X, X >= 0
   a__first(z, z') -{ 1 }-> 1 :|: z' = X, X >= 0, z = 0
   a__first(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2
   a__first(z, z') -{ 1 }-> 1 + mark(Y) + (1 + X + Z) :|: Z >= 0, z = 1 + X, Y >= 0, X >= 0, z' = 1 + Y + Z
   a__sqr(z) -{ 1 }-> 0 :|: z = 0
   a__sqr(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__sqr(z) -{ 1 }-> 1 + (1 + (1 + X) + (1 + X)) :|: z = 1 + X, X >= 0
   a__terms(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__terms(z) -{ 1 }-> 1 + (1 + a__sqr(mark(N))) + (1 + (1 + N)) :|: z = N, N >= 0
   mark(z) -{ 1 }-> a__terms(mark(X)) :|: z = 1 + X, X >= 0
   mark(z) -{ 1 }-> a__sqr(mark(X)) :|: z = 1 + X, X >= 0
   mark(z) -{ 1 }-> a__first(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   mark(z) -{ 1 }-> a__dbl(mark(X)) :|: z = 1 + X, X >= 0
   mark(z) -{ 1 }-> a__add(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   mark(z) -{ 1 }-> 1 :|: z = 1
   mark(z) -{ 1 }-> 0 :|: z = 0
   mark(z) -{ 1 }-> 1 + X :|: z = 1 + X, X >= 0
   mark(z) -{ 1 }-> 1 + mark(X) :|: z = 1 + X, X >= 0
   mark(z) -{ 1 }-> 1 + mark(X1) + X2 :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2

Only complete derivations are relevant for the runtime complexity.

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

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

(24)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__TERMS(z0) -> c(A__SQR(mark(z0)), MARK(z0))
   A__TERMS(z0) -> c1
   A__SQR(0) -> c2
   A__SQR(s(z0)) -> c3
   A__SQR(z0) -> c4
   A__DBL(0) -> c5
   A__DBL(s(z0)) -> c6
   A__DBL(z0) -> c7
   A__ADD(0, z0) -> c8(MARK(z0))
   A__ADD(s(z0), z1) -> c9
   A__ADD(z0, z1) -> c10
   A__FIRST(0, z0) -> c11
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   A__FIRST(z0, z1) -> c13
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(sqr(z0)) -> c15(A__SQR(mark(z0)), MARK(z0))
   MARK(add(z0, z1)) -> c16(A__ADD(mark(z0), mark(z1)), MARK(z0))
   MARK(add(z0, z1)) -> c17(A__ADD(mark(z0), mark(z1)), MARK(z1))
   MARK(dbl(z0)) -> c18(A__DBL(mark(z0)), MARK(z0))
   MARK(first(z0, z1)) -> c19(A__FIRST(mark(z0), mark(z1)), MARK(z0))
   MARK(first(z0, z1)) -> c20(A__FIRST(mark(z0), mark(z1)), MARK(z1))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   MARK(s(z0)) -> c23
   MARK(0) -> c24
   MARK(nil) -> c25
S tuples:
   A__TERMS(z0) -> c(A__SQR(mark(z0)), MARK(z0))
   A__TERMS(z0) -> c1
   A__SQR(0) -> c2
   A__SQR(s(z0)) -> c3
   A__SQR(z0) -> c4
   A__DBL(0) -> c5
   A__DBL(s(z0)) -> c6
   A__DBL(z0) -> c7
   A__ADD(0, z0) -> c8(MARK(z0))
   A__ADD(s(z0), z1) -> c9
   A__ADD(z0, z1) -> c10
   A__FIRST(0, z0) -> c11
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   A__FIRST(z0, z1) -> c13
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(sqr(z0)) -> c15(A__SQR(mark(z0)), MARK(z0))
   MARK(add(z0, z1)) -> c16(A__ADD(mark(z0), mark(z1)), MARK(z0))
   MARK(add(z0, z1)) -> c17(A__ADD(mark(z0), mark(z1)), MARK(z1))
   MARK(dbl(z0)) -> c18(A__DBL(mark(z0)), MARK(z0))
   MARK(first(z0, z1)) -> c19(A__FIRST(mark(z0), mark(z1)), MARK(z0))
   MARK(first(z0, z1)) -> c20(A__FIRST(mark(z0), mark(z1)), MARK(z1))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   MARK(s(z0)) -> c23
   MARK(0) -> c24
   MARK(nil) -> c25
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__TERMS_1, A__SQR_1, A__DBL_1, A__ADD_2, A__FIRST_2, MARK_1

Compound Symbols:   c_2, c1, c2, c3, c4, c5, c6, c7, c8_1, c9, c10, c11, c12_1, c13, c14_2, c15_2, c16_2, c17_2, c18_2, c19_2, c20_2, c21_1, c22_1, c23, c24, c25


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

(25) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 14 trailing nodes:
   A__DBL(s(z0)) -> c6
   A__SQR(s(z0)) -> c3
   MARK(0) -> c24
   A__FIRST(0, z0) -> c11
   MARK(nil) -> c25
   A__SQR(z0) -> c4
   A__ADD(z0, z1) -> c10
   A__DBL(0) -> c5
   A__DBL(z0) -> c7
   A__SQR(0) -> c2
   A__TERMS(z0) -> c1
   MARK(s(z0)) -> c23
   A__FIRST(z0, z1) -> c13
   A__ADD(s(z0), z1) -> c9

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

(26)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__TERMS(z0) -> c(A__SQR(mark(z0)), MARK(z0))
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(sqr(z0)) -> c15(A__SQR(mark(z0)), MARK(z0))
   MARK(add(z0, z1)) -> c16(A__ADD(mark(z0), mark(z1)), MARK(z0))
   MARK(add(z0, z1)) -> c17(A__ADD(mark(z0), mark(z1)), MARK(z1))
   MARK(dbl(z0)) -> c18(A__DBL(mark(z0)), MARK(z0))
   MARK(first(z0, z1)) -> c19(A__FIRST(mark(z0), mark(z1)), MARK(z0))
   MARK(first(z0, z1)) -> c20(A__FIRST(mark(z0), mark(z1)), MARK(z1))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
S tuples:
   A__TERMS(z0) -> c(A__SQR(mark(z0)), MARK(z0))
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(sqr(z0)) -> c15(A__SQR(mark(z0)), MARK(z0))
   MARK(add(z0, z1)) -> c16(A__ADD(mark(z0), mark(z1)), MARK(z0))
   MARK(add(z0, z1)) -> c17(A__ADD(mark(z0), mark(z1)), MARK(z1))
   MARK(dbl(z0)) -> c18(A__DBL(mark(z0)), MARK(z0))
   MARK(first(z0, z1)) -> c19(A__FIRST(mark(z0), mark(z1)), MARK(z0))
   MARK(first(z0, z1)) -> c20(A__FIRST(mark(z0), mark(z1)), MARK(z1))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__TERMS_1, A__ADD_2, A__FIRST_2, MARK_1

Compound Symbols:   c_2, c8_1, c12_1, c14_2, c15_2, c16_2, c17_2, c18_2, c19_2, c20_2, c21_1, c22_1


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

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

(28)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(add(z0, z1)) -> c16(A__ADD(mark(z0), mark(z1)), MARK(z0))
   MARK(add(z0, z1)) -> c17(A__ADD(mark(z0), mark(z1)), MARK(z1))
   MARK(first(z0, z1)) -> c19(A__FIRST(mark(z0), mark(z1)), MARK(z0))
   MARK(first(z0, z1)) -> c20(A__FIRST(mark(z0), mark(z1)), MARK(z1))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(add(z0, z1)) -> c16(A__ADD(mark(z0), mark(z1)), MARK(z0))
   MARK(add(z0, z1)) -> c17(A__ADD(mark(z0), mark(z1)), MARK(z1))
   MARK(first(z0, z1)) -> c19(A__FIRST(mark(z0), mark(z1)), MARK(z0))
   MARK(first(z0, z1)) -> c20(A__FIRST(mark(z0), mark(z1)), MARK(z1))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c16_2, c17_2, c19_2, c20_2, c21_1, c22_1, c_1, c15_1, c18_1


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

(29) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(add(z0, z1)) -> c16(A__ADD(mark(z0), mark(z1)), MARK(z0)) by 
   MARK(add(x0, terms(z0))) -> c16(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(add(x0, sqr(z0))) -> c16(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(add(x0, add(z0, z1))) -> c16(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(add(x0, dbl(z0))) -> c16(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0))
   MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0))
   MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0))
   MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0))
   MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(A__ADD(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(A__ADD(recip(mark(z0)), mark(x1)), MARK(recip(z0)))
   MARK(add(s(z0), x1)) -> c16(A__ADD(s(z0), mark(x1)), MARK(s(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)), MARK(0))
   MARK(add(nil, x1)) -> c16(A__ADD(nil, mark(x1)), MARK(nil))

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

(30)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(add(z0, z1)) -> c17(A__ADD(mark(z0), mark(z1)), MARK(z1))
   MARK(first(z0, z1)) -> c19(A__FIRST(mark(z0), mark(z1)), MARK(z0))
   MARK(first(z0, z1)) -> c20(A__FIRST(mark(z0), mark(z1)), MARK(z1))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(x0, terms(z0))) -> c16(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(add(x0, sqr(z0))) -> c16(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(add(x0, add(z0, z1))) -> c16(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(add(x0, dbl(z0))) -> c16(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0))
   MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0))
   MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0))
   MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0))
   MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(A__ADD(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(A__ADD(recip(mark(z0)), mark(x1)), MARK(recip(z0)))
   MARK(add(s(z0), x1)) -> c16(A__ADD(s(z0), mark(x1)), MARK(s(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)), MARK(0))
   MARK(add(nil, x1)) -> c16(A__ADD(nil, mark(x1)), MARK(nil))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(add(z0, z1)) -> c17(A__ADD(mark(z0), mark(z1)), MARK(z1))
   MARK(first(z0, z1)) -> c19(A__FIRST(mark(z0), mark(z1)), MARK(z0))
   MARK(first(z0, z1)) -> c20(A__FIRST(mark(z0), mark(z1)), MARK(z1))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(x0, terms(z0))) -> c16(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(add(x0, sqr(z0))) -> c16(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(add(x0, add(z0, z1))) -> c16(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(add(x0, dbl(z0))) -> c16(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0))
   MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0))
   MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0))
   MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0))
   MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(A__ADD(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(A__ADD(recip(mark(z0)), mark(x1)), MARK(recip(z0)))
   MARK(add(s(z0), x1)) -> c16(A__ADD(s(z0), mark(x1)), MARK(s(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)), MARK(0))
   MARK(add(nil, x1)) -> c16(A__ADD(nil, mark(x1)), MARK(nil))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c17_2, c19_2, c20_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2


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

(31) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing nodes:
   MARK(add(s(z0), x1)) -> c16(A__ADD(s(z0), mark(x1)), MARK(s(z0)))
   MARK(add(nil, x1)) -> c16(A__ADD(nil, mark(x1)), MARK(nil))

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

(32)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(add(z0, z1)) -> c17(A__ADD(mark(z0), mark(z1)), MARK(z1))
   MARK(first(z0, z1)) -> c19(A__FIRST(mark(z0), mark(z1)), MARK(z0))
   MARK(first(z0, z1)) -> c20(A__FIRST(mark(z0), mark(z1)), MARK(z1))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(x0, terms(z0))) -> c16(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(add(x0, sqr(z0))) -> c16(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(add(x0, add(z0, z1))) -> c16(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(add(x0, dbl(z0))) -> c16(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0))
   MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0))
   MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0))
   MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0))
   MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(A__ADD(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(A__ADD(recip(mark(z0)), mark(x1)), MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)), MARK(0))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(add(z0, z1)) -> c17(A__ADD(mark(z0), mark(z1)), MARK(z1))
   MARK(first(z0, z1)) -> c19(A__FIRST(mark(z0), mark(z1)), MARK(z0))
   MARK(first(z0, z1)) -> c20(A__FIRST(mark(z0), mark(z1)), MARK(z1))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(x0, terms(z0))) -> c16(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(add(x0, sqr(z0))) -> c16(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(add(x0, add(z0, z1))) -> c16(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(add(x0, dbl(z0))) -> c16(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0))
   MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0))
   MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0))
   MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0))
   MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(A__ADD(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(A__ADD(recip(mark(z0)), mark(x1)), MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)), MARK(0))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c17_2, c19_2, c20_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2


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

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

(34)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(add(z0, z1)) -> c17(A__ADD(mark(z0), mark(z1)), MARK(z1))
   MARK(first(z0, z1)) -> c19(A__FIRST(mark(z0), mark(z1)), MARK(z0))
   MARK(first(z0, z1)) -> c20(A__FIRST(mark(z0), mark(z1)), MARK(z1))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(x0, terms(z0))) -> c16(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(add(x0, sqr(z0))) -> c16(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(add(x0, add(z0, z1))) -> c16(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(add(x0, dbl(z0))) -> c16(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0))
   MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0))
   MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0))
   MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0))
   MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(add(z0, z1)) -> c17(A__ADD(mark(z0), mark(z1)), MARK(z1))
   MARK(first(z0, z1)) -> c19(A__FIRST(mark(z0), mark(z1)), MARK(z0))
   MARK(first(z0, z1)) -> c20(A__FIRST(mark(z0), mark(z1)), MARK(z1))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(x0, terms(z0))) -> c16(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(add(x0, sqr(z0))) -> c16(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(add(x0, add(z0, z1))) -> c16(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(add(x0, dbl(z0))) -> c16(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0))
   MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0))
   MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0))
   MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0))
   MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c17_2, c19_2, c20_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1


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

(35) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(add(z0, z1)) -> c17(A__ADD(mark(z0), mark(z1)), MARK(z1)) by 
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)), MARK(s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0), MARK(0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil), MARK(nil))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(cons(z0, z1), x1)) -> c17(A__ADD(cons(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(A__ADD(recip(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(s(z0), x1)) -> c17(A__ADD(s(z0), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(nil, x1)) -> c17(A__ADD(nil, mark(x1)), MARK(x1))

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

(36)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(first(z0, z1)) -> c19(A__FIRST(mark(z0), mark(z1)), MARK(z0))
   MARK(first(z0, z1)) -> c20(A__FIRST(mark(z0), mark(z1)), MARK(z1))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(x0, terms(z0))) -> c16(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(add(x0, sqr(z0))) -> c16(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(add(x0, add(z0, z1))) -> c16(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(add(x0, dbl(z0))) -> c16(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0))
   MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0))
   MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0))
   MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0))
   MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)), MARK(s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0), MARK(0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil), MARK(nil))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(cons(z0, z1), x1)) -> c17(A__ADD(cons(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(A__ADD(recip(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(s(z0), x1)) -> c17(A__ADD(s(z0), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(nil, x1)) -> c17(A__ADD(nil, mark(x1)), MARK(x1))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(first(z0, z1)) -> c19(A__FIRST(mark(z0), mark(z1)), MARK(z0))
   MARK(first(z0, z1)) -> c20(A__FIRST(mark(z0), mark(z1)), MARK(z1))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(x0, terms(z0))) -> c16(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(add(x0, sqr(z0))) -> c16(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(add(x0, add(z0, z1))) -> c16(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(add(x0, dbl(z0))) -> c16(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0))
   MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0))
   MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0))
   MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0))
   MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)), MARK(s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0), MARK(0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil), MARK(nil))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(cons(z0, z1), x1)) -> c17(A__ADD(cons(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(A__ADD(recip(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(s(z0), x1)) -> c17(A__ADD(s(z0), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(nil, x1)) -> c17(A__ADD(nil, mark(x1)), MARK(x1))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c19_2, c20_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2


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

(37) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 7 trailing tuple parts
----------------------------------------

(38)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(first(z0, z1)) -> c19(A__FIRST(mark(z0), mark(z1)), MARK(z0))
   MARK(first(z0, z1)) -> c20(A__FIRST(mark(z0), mark(z1)), MARK(z1))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(x0, terms(z0))) -> c16(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(add(x0, sqr(z0))) -> c16(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(add(x0, add(z0, z1))) -> c16(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(add(x0, dbl(z0))) -> c16(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0))
   MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0))
   MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0))
   MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0))
   MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(first(z0, z1)) -> c19(A__FIRST(mark(z0), mark(z1)), MARK(z0))
   MARK(first(z0, z1)) -> c20(A__FIRST(mark(z0), mark(z1)), MARK(z1))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(x0, terms(z0))) -> c16(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(add(x0, sqr(z0))) -> c16(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(add(x0, add(z0, z1))) -> c16(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(add(x0, dbl(z0))) -> c16(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0))
   MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0))
   MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0))
   MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0))
   MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c19_2, c20_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2, c17_1


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

(39) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(first(z0, z1)) -> c19(A__FIRST(mark(z0), mark(z1)), MARK(z0)) by 
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(x0, recip(z0))) -> c19(A__FIRST(mark(x0), recip(mark(z0))), MARK(x0))
   MARK(first(x0, s(z0))) -> c19(A__FIRST(mark(x0), s(z0)), MARK(x0))
   MARK(first(x0, 0)) -> c19(A__FIRST(mark(x0), 0), MARK(x0))
   MARK(first(x0, nil)) -> c19(A__FIRST(mark(x0), nil), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(cons(z0, z1), x1)) -> c19(A__FIRST(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(A__FIRST(recip(mark(z0)), mark(x1)), MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)), MARK(s(z0)))
   MARK(first(0, x1)) -> c19(A__FIRST(0, mark(x1)), MARK(0))
   MARK(first(nil, x1)) -> c19(A__FIRST(nil, mark(x1)), MARK(nil))

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

(40)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(first(z0, z1)) -> c20(A__FIRST(mark(z0), mark(z1)), MARK(z1))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(x0, terms(z0))) -> c16(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(add(x0, sqr(z0))) -> c16(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(add(x0, add(z0, z1))) -> c16(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(add(x0, dbl(z0))) -> c16(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0))
   MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0))
   MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0))
   MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0))
   MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(x0, recip(z0))) -> c19(A__FIRST(mark(x0), recip(mark(z0))), MARK(x0))
   MARK(first(x0, s(z0))) -> c19(A__FIRST(mark(x0), s(z0)), MARK(x0))
   MARK(first(x0, 0)) -> c19(A__FIRST(mark(x0), 0), MARK(x0))
   MARK(first(x0, nil)) -> c19(A__FIRST(mark(x0), nil), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(cons(z0, z1), x1)) -> c19(A__FIRST(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(A__FIRST(recip(mark(z0)), mark(x1)), MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)), MARK(s(z0)))
   MARK(first(0, x1)) -> c19(A__FIRST(0, mark(x1)), MARK(0))
   MARK(first(nil, x1)) -> c19(A__FIRST(nil, mark(x1)), MARK(nil))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(first(z0, z1)) -> c20(A__FIRST(mark(z0), mark(z1)), MARK(z1))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(x0, terms(z0))) -> c16(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(add(x0, sqr(z0))) -> c16(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(add(x0, add(z0, z1))) -> c16(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(add(x0, dbl(z0))) -> c16(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0))
   MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0))
   MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0))
   MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0))
   MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(x0, recip(z0))) -> c19(A__FIRST(mark(x0), recip(mark(z0))), MARK(x0))
   MARK(first(x0, s(z0))) -> c19(A__FIRST(mark(x0), s(z0)), MARK(x0))
   MARK(first(x0, 0)) -> c19(A__FIRST(mark(x0), 0), MARK(x0))
   MARK(first(x0, nil)) -> c19(A__FIRST(mark(x0), nil), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(cons(z0, z1), x1)) -> c19(A__FIRST(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(A__FIRST(recip(mark(z0)), mark(x1)), MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)), MARK(s(z0)))
   MARK(first(0, x1)) -> c19(A__FIRST(0, mark(x1)), MARK(0))
   MARK(first(nil, x1)) -> c19(A__FIRST(nil, mark(x1)), MARK(nil))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c20_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2, c17_1, c19_2


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

(41) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing nodes:
   MARK(first(0, x1)) -> c19(A__FIRST(0, mark(x1)), MARK(0))
   MARK(first(nil, x1)) -> c19(A__FIRST(nil, mark(x1)), MARK(nil))

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

(42)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(first(z0, z1)) -> c20(A__FIRST(mark(z0), mark(z1)), MARK(z1))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(x0, terms(z0))) -> c16(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(add(x0, sqr(z0))) -> c16(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(add(x0, add(z0, z1))) -> c16(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(add(x0, dbl(z0))) -> c16(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0))
   MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0))
   MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0))
   MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0))
   MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(x0, recip(z0))) -> c19(A__FIRST(mark(x0), recip(mark(z0))), MARK(x0))
   MARK(first(x0, s(z0))) -> c19(A__FIRST(mark(x0), s(z0)), MARK(x0))
   MARK(first(x0, 0)) -> c19(A__FIRST(mark(x0), 0), MARK(x0))
   MARK(first(x0, nil)) -> c19(A__FIRST(mark(x0), nil), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(cons(z0, z1), x1)) -> c19(A__FIRST(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(A__FIRST(recip(mark(z0)), mark(x1)), MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)), MARK(s(z0)))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(first(z0, z1)) -> c20(A__FIRST(mark(z0), mark(z1)), MARK(z1))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(x0, terms(z0))) -> c16(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(add(x0, sqr(z0))) -> c16(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(add(x0, add(z0, z1))) -> c16(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(add(x0, dbl(z0))) -> c16(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0))
   MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0))
   MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0))
   MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0))
   MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(x0, recip(z0))) -> c19(A__FIRST(mark(x0), recip(mark(z0))), MARK(x0))
   MARK(first(x0, s(z0))) -> c19(A__FIRST(mark(x0), s(z0)), MARK(x0))
   MARK(first(x0, 0)) -> c19(A__FIRST(mark(x0), 0), MARK(x0))
   MARK(first(x0, nil)) -> c19(A__FIRST(mark(x0), nil), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(cons(z0, z1), x1)) -> c19(A__FIRST(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(A__FIRST(recip(mark(z0)), mark(x1)), MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)), MARK(s(z0)))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c20_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2, c17_1, c19_2


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

(43) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 7 trailing tuple parts
----------------------------------------

(44)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(first(z0, z1)) -> c20(A__FIRST(mark(z0), mark(z1)), MARK(z1))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(x0, terms(z0))) -> c16(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(add(x0, sqr(z0))) -> c16(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(add(x0, add(z0, z1))) -> c16(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(add(x0, dbl(z0))) -> c16(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0))
   MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0))
   MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0))
   MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0))
   MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(first(z0, z1)) -> c20(A__FIRST(mark(z0), mark(z1)), MARK(z1))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(x0, terms(z0))) -> c16(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(add(x0, sqr(z0))) -> c16(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(add(x0, add(z0, z1))) -> c16(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(add(x0, dbl(z0))) -> c16(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0))
   MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0))
   MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0))
   MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0))
   MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c20_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2, c17_1, c19_2, c19_1


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

(45) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(first(z0, z1)) -> c20(A__FIRST(mark(z0), mark(z1)), MARK(z1)) by 
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(x0, recip(z0))) -> c20(A__FIRST(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(first(x0, s(z0))) -> c20(A__FIRST(mark(x0), s(z0)), MARK(s(z0)))
   MARK(first(x0, 0)) -> c20(A__FIRST(mark(x0), 0), MARK(0))
   MARK(first(x0, nil)) -> c20(A__FIRST(mark(x0), nil), MARK(nil))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(cons(z0, z1), x1)) -> c20(A__FIRST(cons(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(A__FIRST(recip(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(0, x1)) -> c20(A__FIRST(0, mark(x1)), MARK(x1))
   MARK(first(nil, x1)) -> c20(A__FIRST(nil, mark(x1)), MARK(x1))

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

(46)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(x0, terms(z0))) -> c16(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(add(x0, sqr(z0))) -> c16(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(add(x0, add(z0, z1))) -> c16(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(add(x0, dbl(z0))) -> c16(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0))
   MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0))
   MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0))
   MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0))
   MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(x0, recip(z0))) -> c20(A__FIRST(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(first(x0, s(z0))) -> c20(A__FIRST(mark(x0), s(z0)), MARK(s(z0)))
   MARK(first(x0, 0)) -> c20(A__FIRST(mark(x0), 0), MARK(0))
   MARK(first(x0, nil)) -> c20(A__FIRST(mark(x0), nil), MARK(nil))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(cons(z0, z1), x1)) -> c20(A__FIRST(cons(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(A__FIRST(recip(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(0, x1)) -> c20(A__FIRST(0, mark(x1)), MARK(x1))
   MARK(first(nil, x1)) -> c20(A__FIRST(nil, mark(x1)), MARK(x1))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(x0, terms(z0))) -> c16(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(add(x0, sqr(z0))) -> c16(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(add(x0, add(z0, z1))) -> c16(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(add(x0, dbl(z0))) -> c16(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0))
   MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0))
   MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0))
   MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0))
   MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(x0, recip(z0))) -> c20(A__FIRST(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(first(x0, s(z0))) -> c20(A__FIRST(mark(x0), s(z0)), MARK(s(z0)))
   MARK(first(x0, 0)) -> c20(A__FIRST(mark(x0), 0), MARK(0))
   MARK(first(x0, nil)) -> c20(A__FIRST(mark(x0), nil), MARK(nil))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(cons(z0, z1), x1)) -> c20(A__FIRST(cons(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(A__FIRST(recip(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(0, x1)) -> c20(A__FIRST(0, mark(x1)), MARK(x1))
   MARK(first(nil, x1)) -> c20(A__FIRST(nil, mark(x1)), MARK(x1))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2


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

(47) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 3 trailing nodes:
   MARK(first(x0, 0)) -> c20(A__FIRST(mark(x0), 0), MARK(0))
   MARK(first(x0, s(z0))) -> c20(A__FIRST(mark(x0), s(z0)), MARK(s(z0)))
   MARK(first(x0, nil)) -> c20(A__FIRST(mark(x0), nil), MARK(nil))

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

(48)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(x0, terms(z0))) -> c16(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(add(x0, sqr(z0))) -> c16(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(add(x0, add(z0, z1))) -> c16(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(add(x0, dbl(z0))) -> c16(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0))
   MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0))
   MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0))
   MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0))
   MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(x0, recip(z0))) -> c20(A__FIRST(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(cons(z0, z1), x1)) -> c20(A__FIRST(cons(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(A__FIRST(recip(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(0, x1)) -> c20(A__FIRST(0, mark(x1)), MARK(x1))
   MARK(first(nil, x1)) -> c20(A__FIRST(nil, mark(x1)), MARK(x1))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(x0, terms(z0))) -> c16(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(add(x0, sqr(z0))) -> c16(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(add(x0, add(z0, z1))) -> c16(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(add(x0, dbl(z0))) -> c16(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0))
   MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0))
   MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0))
   MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0))
   MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(x0, recip(z0))) -> c20(A__FIRST(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(cons(z0, z1), x1)) -> c20(A__FIRST(cons(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(A__FIRST(recip(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(0, x1)) -> c20(A__FIRST(0, mark(x1)), MARK(x1))
   MARK(first(nil, x1)) -> c20(A__FIRST(nil, mark(x1)), MARK(x1))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2


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

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

(50)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(x0, terms(z0))) -> c16(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(add(x0, sqr(z0))) -> c16(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(add(x0, add(z0, z1))) -> c16(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(add(x0, dbl(z0))) -> c16(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0))
   MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0))
   MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0))
   MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0))
   MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(x0, terms(z0))) -> c16(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(add(x0, sqr(z0))) -> c16(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(add(x0, add(z0, z1))) -> c16(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(add(x0, dbl(z0))) -> c16(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0))
   MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0))
   MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0))
   MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0))
   MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1


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

(51) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(add(x0, terms(z0))) -> c16(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) by 
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(A__ADD(cons(mark(z0), z1), a__terms(mark(x1))), MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(A__ADD(recip(mark(z0)), a__terms(mark(x1))), MARK(recip(z0)))
   MARK(add(s(z0), terms(x1))) -> c16(A__ADD(s(z0), a__terms(mark(x1))), MARK(s(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))), MARK(0))
   MARK(add(nil, terms(x1))) -> c16(A__ADD(nil, a__terms(mark(x1))), MARK(nil))

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

(52)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(x0, sqr(z0))) -> c16(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(add(x0, add(z0, z1))) -> c16(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(add(x0, dbl(z0))) -> c16(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0))
   MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0))
   MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0))
   MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0))
   MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(A__ADD(cons(mark(z0), z1), a__terms(mark(x1))), MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(A__ADD(recip(mark(z0)), a__terms(mark(x1))), MARK(recip(z0)))
   MARK(add(s(z0), terms(x1))) -> c16(A__ADD(s(z0), a__terms(mark(x1))), MARK(s(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))), MARK(0))
   MARK(add(nil, terms(x1))) -> c16(A__ADD(nil, a__terms(mark(x1))), MARK(nil))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(x0, sqr(z0))) -> c16(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(add(x0, add(z0, z1))) -> c16(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(add(x0, dbl(z0))) -> c16(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0))
   MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0))
   MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0))
   MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0))
   MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(A__ADD(cons(mark(z0), z1), a__terms(mark(x1))), MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(A__ADD(recip(mark(z0)), a__terms(mark(x1))), MARK(recip(z0)))
   MARK(add(s(z0), terms(x1))) -> c16(A__ADD(s(z0), a__terms(mark(x1))), MARK(s(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))), MARK(0))
   MARK(add(nil, terms(x1))) -> c16(A__ADD(nil, a__terms(mark(x1))), MARK(nil))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1


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

(53) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing nodes:
   MARK(add(nil, terms(x1))) -> c16(A__ADD(nil, a__terms(mark(x1))), MARK(nil))
   MARK(add(s(z0), terms(x1))) -> c16(A__ADD(s(z0), a__terms(mark(x1))), MARK(s(z0)))

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

(54)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(x0, sqr(z0))) -> c16(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(add(x0, add(z0, z1))) -> c16(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(add(x0, dbl(z0))) -> c16(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0))
   MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0))
   MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0))
   MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0))
   MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(A__ADD(cons(mark(z0), z1), a__terms(mark(x1))), MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(A__ADD(recip(mark(z0)), a__terms(mark(x1))), MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))), MARK(0))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(x0, sqr(z0))) -> c16(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(add(x0, add(z0, z1))) -> c16(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(add(x0, dbl(z0))) -> c16(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0))
   MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0))
   MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0))
   MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0))
   MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(A__ADD(cons(mark(z0), z1), a__terms(mark(x1))), MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(A__ADD(recip(mark(z0)), a__terms(mark(x1))), MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))), MARK(0))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1


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

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

(56)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(x0, sqr(z0))) -> c16(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(add(x0, add(z0, z1))) -> c16(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(add(x0, dbl(z0))) -> c16(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0))
   MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0))
   MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0))
   MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0))
   MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(x0, sqr(z0))) -> c16(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(add(x0, add(z0, z1))) -> c16(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(add(x0, dbl(z0))) -> c16(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0))
   MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0))
   MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0))
   MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0))
   MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1


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

(57) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(add(x0, sqr(z0))) -> c16(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) by 
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(A__ADD(cons(mark(z0), z1), a__sqr(mark(x1))), MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(A__ADD(recip(mark(z0)), a__sqr(mark(x1))), MARK(recip(z0)))
   MARK(add(s(z0), sqr(x1))) -> c16(A__ADD(s(z0), a__sqr(mark(x1))), MARK(s(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))), MARK(0))
   MARK(add(nil, sqr(x1))) -> c16(A__ADD(nil, a__sqr(mark(x1))), MARK(nil))

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

(58)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(x0, add(z0, z1))) -> c16(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(add(x0, dbl(z0))) -> c16(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0))
   MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0))
   MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0))
   MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0))
   MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(A__ADD(cons(mark(z0), z1), a__sqr(mark(x1))), MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(A__ADD(recip(mark(z0)), a__sqr(mark(x1))), MARK(recip(z0)))
   MARK(add(s(z0), sqr(x1))) -> c16(A__ADD(s(z0), a__sqr(mark(x1))), MARK(s(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))), MARK(0))
   MARK(add(nil, sqr(x1))) -> c16(A__ADD(nil, a__sqr(mark(x1))), MARK(nil))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(x0, add(z0, z1))) -> c16(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(add(x0, dbl(z0))) -> c16(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0))
   MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0))
   MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0))
   MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0))
   MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(A__ADD(cons(mark(z0), z1), a__sqr(mark(x1))), MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(A__ADD(recip(mark(z0)), a__sqr(mark(x1))), MARK(recip(z0)))
   MARK(add(s(z0), sqr(x1))) -> c16(A__ADD(s(z0), a__sqr(mark(x1))), MARK(s(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))), MARK(0))
   MARK(add(nil, sqr(x1))) -> c16(A__ADD(nil, a__sqr(mark(x1))), MARK(nil))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1


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

(59) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing nodes:
   MARK(add(s(z0), sqr(x1))) -> c16(A__ADD(s(z0), a__sqr(mark(x1))), MARK(s(z0)))
   MARK(add(nil, sqr(x1))) -> c16(A__ADD(nil, a__sqr(mark(x1))), MARK(nil))

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

(60)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(x0, add(z0, z1))) -> c16(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(add(x0, dbl(z0))) -> c16(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0))
   MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0))
   MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0))
   MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0))
   MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(A__ADD(cons(mark(z0), z1), a__sqr(mark(x1))), MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(A__ADD(recip(mark(z0)), a__sqr(mark(x1))), MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))), MARK(0))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(x0, add(z0, z1))) -> c16(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(add(x0, dbl(z0))) -> c16(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0))
   MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0))
   MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0))
   MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0))
   MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(A__ADD(cons(mark(z0), z1), a__sqr(mark(x1))), MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(A__ADD(recip(mark(z0)), a__sqr(mark(x1))), MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))), MARK(0))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1


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

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

(62)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(x0, add(z0, z1))) -> c16(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(add(x0, dbl(z0))) -> c16(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0))
   MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0))
   MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0))
   MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0))
   MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(x0, add(z0, z1))) -> c16(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(add(x0, dbl(z0))) -> c16(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0))
   MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0))
   MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0))
   MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0))
   MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1


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

(63) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(add(x0, add(z0, z1))) -> c16(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) by 
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), add(x1, x2))) -> c16(A__ADD(cons(mark(z0), z1), a__add(mark(x1), mark(x2))), MARK(cons(z0, z1)))
   MARK(add(recip(z0), add(x1, x2))) -> c16(A__ADD(recip(mark(z0)), a__add(mark(x1), mark(x2))), MARK(recip(z0)))
   MARK(add(s(z0), add(x1, x2))) -> c16(A__ADD(s(z0), a__add(mark(x1), mark(x2))), MARK(s(z0)))
   MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2))), MARK(0))
   MARK(add(nil, add(x1, x2))) -> c16(A__ADD(nil, a__add(mark(x1), mark(x2))), MARK(nil))

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

(64)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(x0, dbl(z0))) -> c16(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0))
   MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0))
   MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0))
   MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0))
   MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), add(x1, x2))) -> c16(A__ADD(cons(mark(z0), z1), a__add(mark(x1), mark(x2))), MARK(cons(z0, z1)))
   MARK(add(recip(z0), add(x1, x2))) -> c16(A__ADD(recip(mark(z0)), a__add(mark(x1), mark(x2))), MARK(recip(z0)))
   MARK(add(s(z0), add(x1, x2))) -> c16(A__ADD(s(z0), a__add(mark(x1), mark(x2))), MARK(s(z0)))
   MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2))), MARK(0))
   MARK(add(nil, add(x1, x2))) -> c16(A__ADD(nil, a__add(mark(x1), mark(x2))), MARK(nil))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(x0, dbl(z0))) -> c16(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0))
   MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0))
   MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0))
   MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0))
   MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), add(x1, x2))) -> c16(A__ADD(cons(mark(z0), z1), a__add(mark(x1), mark(x2))), MARK(cons(z0, z1)))
   MARK(add(recip(z0), add(x1, x2))) -> c16(A__ADD(recip(mark(z0)), a__add(mark(x1), mark(x2))), MARK(recip(z0)))
   MARK(add(s(z0), add(x1, x2))) -> c16(A__ADD(s(z0), a__add(mark(x1), mark(x2))), MARK(s(z0)))
   MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2))), MARK(0))
   MARK(add(nil, add(x1, x2))) -> c16(A__ADD(nil, a__add(mark(x1), mark(x2))), MARK(nil))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1


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

(65) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing nodes:
   MARK(add(s(z0), add(x1, x2))) -> c16(A__ADD(s(z0), a__add(mark(x1), mark(x2))), MARK(s(z0)))
   MARK(add(nil, add(x1, x2))) -> c16(A__ADD(nil, a__add(mark(x1), mark(x2))), MARK(nil))

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

(66)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(x0, dbl(z0))) -> c16(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0))
   MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0))
   MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0))
   MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0))
   MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), add(x1, x2))) -> c16(A__ADD(cons(mark(z0), z1), a__add(mark(x1), mark(x2))), MARK(cons(z0, z1)))
   MARK(add(recip(z0), add(x1, x2))) -> c16(A__ADD(recip(mark(z0)), a__add(mark(x1), mark(x2))), MARK(recip(z0)))
   MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2))), MARK(0))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(x0, dbl(z0))) -> c16(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0))
   MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0))
   MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0))
   MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0))
   MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), add(x1, x2))) -> c16(A__ADD(cons(mark(z0), z1), a__add(mark(x1), mark(x2))), MARK(cons(z0, z1)))
   MARK(add(recip(z0), add(x1, x2))) -> c16(A__ADD(recip(mark(z0)), a__add(mark(x1), mark(x2))), MARK(recip(z0)))
   MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2))), MARK(0))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1


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

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

(68)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(x0, dbl(z0))) -> c16(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0))
   MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0))
   MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0))
   MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0))
   MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2))))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(x0, dbl(z0))) -> c16(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0))
   MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0))
   MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0))
   MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0))
   MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2))))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1


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

(69) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(add(x0, dbl(z0))) -> c16(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) by 
   MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0))
   MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0))
   MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0))
   MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0))
   MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), dbl(x1))) -> c16(A__ADD(cons(mark(z0), z1), a__dbl(mark(x1))), MARK(cons(z0, z1)))
   MARK(add(recip(z0), dbl(x1))) -> c16(A__ADD(recip(mark(z0)), a__dbl(mark(x1))), MARK(recip(z0)))
   MARK(add(s(z0), dbl(x1))) -> c16(A__ADD(s(z0), a__dbl(mark(x1))), MARK(s(z0)))
   MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1))), MARK(0))
   MARK(add(nil, dbl(x1))) -> c16(A__ADD(nil, a__dbl(mark(x1))), MARK(nil))

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

(70)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0))
   MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0))
   MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0))
   MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0))
   MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2))))
   MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0))
   MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0))
   MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0))
   MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0))
   MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), dbl(x1))) -> c16(A__ADD(cons(mark(z0), z1), a__dbl(mark(x1))), MARK(cons(z0, z1)))
   MARK(add(recip(z0), dbl(x1))) -> c16(A__ADD(recip(mark(z0)), a__dbl(mark(x1))), MARK(recip(z0)))
   MARK(add(s(z0), dbl(x1))) -> c16(A__ADD(s(z0), a__dbl(mark(x1))), MARK(s(z0)))
   MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1))), MARK(0))
   MARK(add(nil, dbl(x1))) -> c16(A__ADD(nil, a__dbl(mark(x1))), MARK(nil))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0))
   MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0))
   MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0))
   MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0))
   MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2))))
   MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0))
   MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0))
   MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0))
   MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0))
   MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), dbl(x1))) -> c16(A__ADD(cons(mark(z0), z1), a__dbl(mark(x1))), MARK(cons(z0, z1)))
   MARK(add(recip(z0), dbl(x1))) -> c16(A__ADD(recip(mark(z0)), a__dbl(mark(x1))), MARK(recip(z0)))
   MARK(add(s(z0), dbl(x1))) -> c16(A__ADD(s(z0), a__dbl(mark(x1))), MARK(s(z0)))
   MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1))), MARK(0))
   MARK(add(nil, dbl(x1))) -> c16(A__ADD(nil, a__dbl(mark(x1))), MARK(nil))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1


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

(71) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing nodes:
   MARK(add(s(z0), dbl(x1))) -> c16(A__ADD(s(z0), a__dbl(mark(x1))), MARK(s(z0)))
   MARK(add(nil, dbl(x1))) -> c16(A__ADD(nil, a__dbl(mark(x1))), MARK(nil))

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

(72)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0))
   MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0))
   MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0))
   MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0))
   MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2))))
   MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0))
   MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0))
   MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0))
   MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0))
   MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), dbl(x1))) -> c16(A__ADD(cons(mark(z0), z1), a__dbl(mark(x1))), MARK(cons(z0, z1)))
   MARK(add(recip(z0), dbl(x1))) -> c16(A__ADD(recip(mark(z0)), a__dbl(mark(x1))), MARK(recip(z0)))
   MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1))), MARK(0))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0))
   MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0))
   MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0))
   MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0))
   MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2))))
   MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0))
   MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0))
   MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0))
   MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0))
   MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), dbl(x1))) -> c16(A__ADD(cons(mark(z0), z1), a__dbl(mark(x1))), MARK(cons(z0, z1)))
   MARK(add(recip(z0), dbl(x1))) -> c16(A__ADD(recip(mark(z0)), a__dbl(mark(x1))), MARK(recip(z0)))
   MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1))), MARK(0))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1


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

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

(74)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0))
   MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0))
   MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0))
   MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0))
   MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2))))
   MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0))
   MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0))
   MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0))
   MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0))
   MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1))))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0))
   MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0))
   MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0))
   MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0))
   MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2))))
   MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0))
   MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0))
   MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0))
   MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0))
   MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1))))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1


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

(75) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) by 
   MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0))
   MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0))
   MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0))
   MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), first(x1, x2))) -> c16(A__ADD(cons(mark(z0), z1), a__first(mark(x1), mark(x2))), MARK(cons(z0, z1)))
   MARK(add(recip(z0), first(x1, x2))) -> c16(A__ADD(recip(mark(z0)), a__first(mark(x1), mark(x2))), MARK(recip(z0)))
   MARK(add(s(z0), first(x1, x2))) -> c16(A__ADD(s(z0), a__first(mark(x1), mark(x2))), MARK(s(z0)))
   MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2))), MARK(0))
   MARK(add(nil, first(x1, x2))) -> c16(A__ADD(nil, a__first(mark(x1), mark(x2))), MARK(nil))

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

(76)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0))
   MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0))
   MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0))
   MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0))
   MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2))))
   MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0))
   MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0))
   MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0))
   MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0))
   MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1))))
   MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0))
   MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0))
   MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0))
   MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), first(x1, x2))) -> c16(A__ADD(cons(mark(z0), z1), a__first(mark(x1), mark(x2))), MARK(cons(z0, z1)))
   MARK(add(recip(z0), first(x1, x2))) -> c16(A__ADD(recip(mark(z0)), a__first(mark(x1), mark(x2))), MARK(recip(z0)))
   MARK(add(s(z0), first(x1, x2))) -> c16(A__ADD(s(z0), a__first(mark(x1), mark(x2))), MARK(s(z0)))
   MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2))), MARK(0))
   MARK(add(nil, first(x1, x2))) -> c16(A__ADD(nil, a__first(mark(x1), mark(x2))), MARK(nil))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0))
   MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0))
   MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0))
   MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0))
   MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2))))
   MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0))
   MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0))
   MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0))
   MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0))
   MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1))))
   MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0))
   MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0))
   MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0))
   MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), first(x1, x2))) -> c16(A__ADD(cons(mark(z0), z1), a__first(mark(x1), mark(x2))), MARK(cons(z0, z1)))
   MARK(add(recip(z0), first(x1, x2))) -> c16(A__ADD(recip(mark(z0)), a__first(mark(x1), mark(x2))), MARK(recip(z0)))
   MARK(add(s(z0), first(x1, x2))) -> c16(A__ADD(s(z0), a__first(mark(x1), mark(x2))), MARK(s(z0)))
   MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2))), MARK(0))
   MARK(add(nil, first(x1, x2))) -> c16(A__ADD(nil, a__first(mark(x1), mark(x2))), MARK(nil))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1


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

(77) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing nodes:
   MARK(add(s(z0), first(x1, x2))) -> c16(A__ADD(s(z0), a__first(mark(x1), mark(x2))), MARK(s(z0)))
   MARK(add(nil, first(x1, x2))) -> c16(A__ADD(nil, a__first(mark(x1), mark(x2))), MARK(nil))

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

(78)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0))
   MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0))
   MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0))
   MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0))
   MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2))))
   MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0))
   MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0))
   MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0))
   MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0))
   MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1))))
   MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0))
   MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0))
   MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0))
   MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), first(x1, x2))) -> c16(A__ADD(cons(mark(z0), z1), a__first(mark(x1), mark(x2))), MARK(cons(z0, z1)))
   MARK(add(recip(z0), first(x1, x2))) -> c16(A__ADD(recip(mark(z0)), a__first(mark(x1), mark(x2))), MARK(recip(z0)))
   MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2))), MARK(0))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0))
   MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0))
   MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0))
   MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0))
   MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2))))
   MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0))
   MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0))
   MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0))
   MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0))
   MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1))))
   MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0))
   MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0))
   MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0))
   MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), first(x1, x2))) -> c16(A__ADD(cons(mark(z0), z1), a__first(mark(x1), mark(x2))), MARK(cons(z0, z1)))
   MARK(add(recip(z0), first(x1, x2))) -> c16(A__ADD(recip(mark(z0)), a__first(mark(x1), mark(x2))), MARK(recip(z0)))
   MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2))), MARK(0))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1


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

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

(80)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0))
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   MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0))
   MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2))))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0))
   MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0))
   MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0))
   MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0))
   MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2))))
   MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0))
   MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0))
   MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0))
   MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0))
   MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1))))
   MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0))
   MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0))
   MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0))
   MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2))))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1


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

(81) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) by 
   MARK(add(x0, cons(terms(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(sqr(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0))
   MARK(add(x0, cons(dbl(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0))
   MARK(add(x0, cons(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0))
   MARK(add(x0, cons(recip(z0), x2))) -> c16(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(s(z0), x2))) -> c16(A__ADD(mark(x0), cons(s(z0), x2)), MARK(x0))
   MARK(add(x0, cons(0, x2))) -> c16(A__ADD(mark(x0), cons(0, x2)), MARK(x0))
   MARK(add(x0, cons(nil, x2))) -> c16(A__ADD(mark(x0), cons(nil, x2)), MARK(x0))
   MARK(add(terms(z0), cons(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(terms(z0)))
   MARK(add(sqr(z0), cons(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), cons(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), cons(x1, x2))) -> c16(A__ADD(cons(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(z0, z1)))
   MARK(add(recip(z0), cons(x1, x2))) -> c16(A__ADD(recip(mark(z0)), cons(mark(x1), x2)), MARK(recip(z0)))
   MARK(add(s(z0), cons(x1, x2))) -> c16(A__ADD(s(z0), cons(mark(x1), x2)), MARK(s(z0)))
   MARK(add(0, cons(x1, x2))) -> c16(A__ADD(0, cons(mark(x1), x2)), MARK(0))
   MARK(add(nil, cons(x1, x2))) -> c16(A__ADD(nil, cons(mark(x1), x2)), MARK(nil))

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

(82)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0))
   MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0))
   MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0))
   MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0))
   MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2))))
   MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0))
   MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0))
   MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0))
   MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0))
   MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1))))
   MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0))
   MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0))
   MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0))
   MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2))))
   MARK(add(x0, cons(terms(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(sqr(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0))
   MARK(add(x0, cons(dbl(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0))
   MARK(add(x0, cons(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0))
   MARK(add(x0, cons(recip(z0), x2))) -> c16(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(s(z0), x2))) -> c16(A__ADD(mark(x0), cons(s(z0), x2)), MARK(x0))
   MARK(add(x0, cons(0, x2))) -> c16(A__ADD(mark(x0), cons(0, x2)), MARK(x0))
   MARK(add(x0, cons(nil, x2))) -> c16(A__ADD(mark(x0), cons(nil, x2)), MARK(x0))
   MARK(add(terms(z0), cons(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(terms(z0)))
   MARK(add(sqr(z0), cons(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), cons(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), cons(x1, x2))) -> c16(A__ADD(cons(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(z0, z1)))
   MARK(add(recip(z0), cons(x1, x2))) -> c16(A__ADD(recip(mark(z0)), cons(mark(x1), x2)), MARK(recip(z0)))
   MARK(add(s(z0), cons(x1, x2))) -> c16(A__ADD(s(z0), cons(mark(x1), x2)), MARK(s(z0)))
   MARK(add(0, cons(x1, x2))) -> c16(A__ADD(0, cons(mark(x1), x2)), MARK(0))
   MARK(add(nil, cons(x1, x2))) -> c16(A__ADD(nil, cons(mark(x1), x2)), MARK(nil))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0))
   MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0))
   MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0))
   MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0))
   MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2))))
   MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0))
   MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0))
   MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0))
   MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0))
   MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1))))
   MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0))
   MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0))
   MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0))
   MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2))))
   MARK(add(x0, cons(terms(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(sqr(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0))
   MARK(add(x0, cons(dbl(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0))
   MARK(add(x0, cons(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0))
   MARK(add(x0, cons(recip(z0), x2))) -> c16(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(s(z0), x2))) -> c16(A__ADD(mark(x0), cons(s(z0), x2)), MARK(x0))
   MARK(add(x0, cons(0, x2))) -> c16(A__ADD(mark(x0), cons(0, x2)), MARK(x0))
   MARK(add(x0, cons(nil, x2))) -> c16(A__ADD(mark(x0), cons(nil, x2)), MARK(x0))
   MARK(add(terms(z0), cons(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(terms(z0)))
   MARK(add(sqr(z0), cons(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), cons(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), cons(x1, x2))) -> c16(A__ADD(cons(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(z0, z1)))
   MARK(add(recip(z0), cons(x1, x2))) -> c16(A__ADD(recip(mark(z0)), cons(mark(x1), x2)), MARK(recip(z0)))
   MARK(add(s(z0), cons(x1, x2))) -> c16(A__ADD(s(z0), cons(mark(x1), x2)), MARK(s(z0)))
   MARK(add(0, cons(x1, x2))) -> c16(A__ADD(0, cons(mark(x1), x2)), MARK(0))
   MARK(add(nil, cons(x1, x2))) -> c16(A__ADD(nil, cons(mark(x1), x2)), MARK(nil))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1


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

(83) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing nodes:
   MARK(add(nil, cons(x1, x2))) -> c16(A__ADD(nil, cons(mark(x1), x2)), MARK(nil))
   MARK(add(s(z0), cons(x1, x2))) -> c16(A__ADD(s(z0), cons(mark(x1), x2)), MARK(s(z0)))

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

(84)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
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   MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0))
   MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2))))
   MARK(add(x0, cons(terms(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(sqr(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0))
   MARK(add(x0, cons(dbl(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0))
   MARK(add(x0, cons(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0))
   MARK(add(x0, cons(recip(z0), x2))) -> c16(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(s(z0), x2))) -> c16(A__ADD(mark(x0), cons(s(z0), x2)), MARK(x0))
   MARK(add(x0, cons(0, x2))) -> c16(A__ADD(mark(x0), cons(0, x2)), MARK(x0))
   MARK(add(x0, cons(nil, x2))) -> c16(A__ADD(mark(x0), cons(nil, x2)), MARK(x0))
   MARK(add(terms(z0), cons(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(terms(z0)))
   MARK(add(sqr(z0), cons(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), cons(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), cons(x1, x2))) -> c16(A__ADD(cons(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(z0, z1)))
   MARK(add(recip(z0), cons(x1, x2))) -> c16(A__ADD(recip(mark(z0)), cons(mark(x1), x2)), MARK(recip(z0)))
   MARK(add(0, cons(x1, x2))) -> c16(A__ADD(0, cons(mark(x1), x2)), MARK(0))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0))
   MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0))
   MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0))
   MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0))
   MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2))))
   MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0))
   MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0))
   MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0))
   MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0))
   MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1))))
   MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0))
   MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0))
   MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0))
   MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2))))
   MARK(add(x0, cons(terms(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(sqr(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0))
   MARK(add(x0, cons(dbl(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0))
   MARK(add(x0, cons(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0))
   MARK(add(x0, cons(recip(z0), x2))) -> c16(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(s(z0), x2))) -> c16(A__ADD(mark(x0), cons(s(z0), x2)), MARK(x0))
   MARK(add(x0, cons(0, x2))) -> c16(A__ADD(mark(x0), cons(0, x2)), MARK(x0))
   MARK(add(x0, cons(nil, x2))) -> c16(A__ADD(mark(x0), cons(nil, x2)), MARK(x0))
   MARK(add(terms(z0), cons(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(terms(z0)))
   MARK(add(sqr(z0), cons(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), cons(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), cons(x1, x2))) -> c16(A__ADD(cons(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(z0, z1)))
   MARK(add(recip(z0), cons(x1, x2))) -> c16(A__ADD(recip(mark(z0)), cons(mark(x1), x2)), MARK(recip(z0)))
   MARK(add(0, cons(x1, x2))) -> c16(A__ADD(0, cons(mark(x1), x2)), MARK(0))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1


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

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

(86)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0))
   MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0))
   MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0))
   MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0))
   MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2))))
   MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0))
   MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0))
   MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0))
   MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0))
   MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1))))
   MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0))
   MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0))
   MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0))
   MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2))))
   MARK(add(x0, cons(terms(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(sqr(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0))
   MARK(add(x0, cons(dbl(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0))
   MARK(add(x0, cons(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0))
   MARK(add(x0, cons(recip(z0), x2))) -> c16(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(s(z0), x2))) -> c16(A__ADD(mark(x0), cons(s(z0), x2)), MARK(x0))
   MARK(add(x0, cons(0, x2))) -> c16(A__ADD(mark(x0), cons(0, x2)), MARK(x0))
   MARK(add(x0, cons(nil, x2))) -> c16(A__ADD(mark(x0), cons(nil, x2)), MARK(x0))
   MARK(add(terms(z0), cons(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(terms(z0)))
   MARK(add(sqr(z0), cons(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), cons(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), cons(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), cons(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, cons(x1, x2))) -> c16(A__ADD(0, cons(mark(x1), x2)))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0))
   MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0))
   MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0))
   MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0))
   MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2))))
   MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0))
   MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0))
   MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0))
   MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0))
   MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1))))
   MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0))
   MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0))
   MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0))
   MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2))))
   MARK(add(x0, cons(terms(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(sqr(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0))
   MARK(add(x0, cons(dbl(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0))
   MARK(add(x0, cons(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0))
   MARK(add(x0, cons(recip(z0), x2))) -> c16(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(s(z0), x2))) -> c16(A__ADD(mark(x0), cons(s(z0), x2)), MARK(x0))
   MARK(add(x0, cons(0, x2))) -> c16(A__ADD(mark(x0), cons(0, x2)), MARK(x0))
   MARK(add(x0, cons(nil, x2))) -> c16(A__ADD(mark(x0), cons(nil, x2)), MARK(x0))
   MARK(add(terms(z0), cons(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(terms(z0)))
   MARK(add(sqr(z0), cons(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), cons(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), cons(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), cons(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, cons(x1, x2))) -> c16(A__ADD(0, cons(mark(x1), x2)))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1


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

(87) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) by 
   MARK(add(x0, recip(terms(z0)))) -> c16(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(sqr(z0)))) -> c16(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(add(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, recip(dbl(z0)))) -> c16(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(first(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, recip(cons(z0, z1)))) -> c16(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, recip(recip(z0)))) -> c16(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(s(z0)))) -> c16(A__ADD(mark(x0), recip(s(z0))), MARK(x0))
   MARK(add(x0, recip(0))) -> c16(A__ADD(mark(x0), recip(0)), MARK(x0))
   MARK(add(x0, recip(nil))) -> c16(A__ADD(mark(x0), recip(nil)), MARK(x0))
   MARK(add(terms(z0), recip(x1))) -> c16(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), recip(x1))) -> c16(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), recip(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), recip(x1))) -> c16(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), recip(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), recip(x1))) -> c16(A__ADD(cons(mark(z0), z1), recip(mark(x1))), MARK(cons(z0, z1)))
   MARK(add(recip(z0), recip(x1))) -> c16(A__ADD(recip(mark(z0)), recip(mark(x1))), MARK(recip(z0)))
   MARK(add(s(z0), recip(x1))) -> c16(A__ADD(s(z0), recip(mark(x1))), MARK(s(z0)))
   MARK(add(0, recip(x1))) -> c16(A__ADD(0, recip(mark(x1))), MARK(0))
   MARK(add(nil, recip(x1))) -> c16(A__ADD(nil, recip(mark(x1))), MARK(nil))

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

(88)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0))
   MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0))
   MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0))
   MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2))))
   MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0))
   MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0))
   MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0))
   MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0))
   MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1))))
   MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0))
   MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0))
   MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0))
   MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2))))
   MARK(add(x0, cons(terms(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(sqr(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0))
   MARK(add(x0, cons(dbl(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0))
   MARK(add(x0, cons(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0))
   MARK(add(x0, cons(recip(z0), x2))) -> c16(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(s(z0), x2))) -> c16(A__ADD(mark(x0), cons(s(z0), x2)), MARK(x0))
   MARK(add(x0, cons(0, x2))) -> c16(A__ADD(mark(x0), cons(0, x2)), MARK(x0))
   MARK(add(x0, cons(nil, x2))) -> c16(A__ADD(mark(x0), cons(nil, x2)), MARK(x0))
   MARK(add(terms(z0), cons(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(terms(z0)))
   MARK(add(sqr(z0), cons(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), cons(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), cons(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), cons(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, cons(x1, x2))) -> c16(A__ADD(0, cons(mark(x1), x2)))
   MARK(add(x0, recip(terms(z0)))) -> c16(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(sqr(z0)))) -> c16(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(add(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, recip(dbl(z0)))) -> c16(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(first(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, recip(cons(z0, z1)))) -> c16(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, recip(recip(z0)))) -> c16(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(s(z0)))) -> c16(A__ADD(mark(x0), recip(s(z0))), MARK(x0))
   MARK(add(x0, recip(0))) -> c16(A__ADD(mark(x0), recip(0)), MARK(x0))
   MARK(add(x0, recip(nil))) -> c16(A__ADD(mark(x0), recip(nil)), MARK(x0))
   MARK(add(terms(z0), recip(x1))) -> c16(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), recip(x1))) -> c16(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), recip(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), recip(x1))) -> c16(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), recip(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), recip(x1))) -> c16(A__ADD(cons(mark(z0), z1), recip(mark(x1))), MARK(cons(z0, z1)))
   MARK(add(recip(z0), recip(x1))) -> c16(A__ADD(recip(mark(z0)), recip(mark(x1))), MARK(recip(z0)))
   MARK(add(s(z0), recip(x1))) -> c16(A__ADD(s(z0), recip(mark(x1))), MARK(s(z0)))
   MARK(add(0, recip(x1))) -> c16(A__ADD(0, recip(mark(x1))), MARK(0))
   MARK(add(nil, recip(x1))) -> c16(A__ADD(nil, recip(mark(x1))), MARK(nil))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0))
   MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0))
   MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0))
   MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2))))
   MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0))
   MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0))
   MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0))
   MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0))
   MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1))))
   MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0))
   MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0))
   MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0))
   MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2))))
   MARK(add(x0, cons(terms(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(sqr(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0))
   MARK(add(x0, cons(dbl(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0))
   MARK(add(x0, cons(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0))
   MARK(add(x0, cons(recip(z0), x2))) -> c16(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(s(z0), x2))) -> c16(A__ADD(mark(x0), cons(s(z0), x2)), MARK(x0))
   MARK(add(x0, cons(0, x2))) -> c16(A__ADD(mark(x0), cons(0, x2)), MARK(x0))
   MARK(add(x0, cons(nil, x2))) -> c16(A__ADD(mark(x0), cons(nil, x2)), MARK(x0))
   MARK(add(terms(z0), cons(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(terms(z0)))
   MARK(add(sqr(z0), cons(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), cons(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), cons(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), cons(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, cons(x1, x2))) -> c16(A__ADD(0, cons(mark(x1), x2)))
   MARK(add(x0, recip(terms(z0)))) -> c16(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(sqr(z0)))) -> c16(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(add(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, recip(dbl(z0)))) -> c16(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(first(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, recip(cons(z0, z1)))) -> c16(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, recip(recip(z0)))) -> c16(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(s(z0)))) -> c16(A__ADD(mark(x0), recip(s(z0))), MARK(x0))
   MARK(add(x0, recip(0))) -> c16(A__ADD(mark(x0), recip(0)), MARK(x0))
   MARK(add(x0, recip(nil))) -> c16(A__ADD(mark(x0), recip(nil)), MARK(x0))
   MARK(add(terms(z0), recip(x1))) -> c16(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), recip(x1))) -> c16(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), recip(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), recip(x1))) -> c16(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), recip(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), recip(x1))) -> c16(A__ADD(cons(mark(z0), z1), recip(mark(x1))), MARK(cons(z0, z1)))
   MARK(add(recip(z0), recip(x1))) -> c16(A__ADD(recip(mark(z0)), recip(mark(x1))), MARK(recip(z0)))
   MARK(add(s(z0), recip(x1))) -> c16(A__ADD(s(z0), recip(mark(x1))), MARK(s(z0)))
   MARK(add(0, recip(x1))) -> c16(A__ADD(0, recip(mark(x1))), MARK(0))
   MARK(add(nil, recip(x1))) -> c16(A__ADD(nil, recip(mark(x1))), MARK(nil))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1


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

(89) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing nodes:
   MARK(add(nil, recip(x1))) -> c16(A__ADD(nil, recip(mark(x1))), MARK(nil))
   MARK(add(s(z0), recip(x1))) -> c16(A__ADD(s(z0), recip(mark(x1))), MARK(s(z0)))

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

(90)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0))
   MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0))
   MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0))
   MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
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   MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2))))
   MARK(add(x0, cons(terms(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(sqr(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0))
   MARK(add(x0, cons(dbl(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0))
   MARK(add(x0, cons(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0))
   MARK(add(x0, cons(recip(z0), x2))) -> c16(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(s(z0), x2))) -> c16(A__ADD(mark(x0), cons(s(z0), x2)), MARK(x0))
   MARK(add(x0, cons(0, x2))) -> c16(A__ADD(mark(x0), cons(0, x2)), MARK(x0))
   MARK(add(x0, cons(nil, x2))) -> c16(A__ADD(mark(x0), cons(nil, x2)), MARK(x0))
   MARK(add(terms(z0), cons(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(terms(z0)))
   MARK(add(sqr(z0), cons(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), cons(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), cons(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), cons(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, cons(x1, x2))) -> c16(A__ADD(0, cons(mark(x1), x2)))
   MARK(add(x0, recip(terms(z0)))) -> c16(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(sqr(z0)))) -> c16(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(add(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, recip(dbl(z0)))) -> c16(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(first(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, recip(cons(z0, z1)))) -> c16(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, recip(recip(z0)))) -> c16(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(s(z0)))) -> c16(A__ADD(mark(x0), recip(s(z0))), MARK(x0))
   MARK(add(x0, recip(0))) -> c16(A__ADD(mark(x0), recip(0)), MARK(x0))
   MARK(add(x0, recip(nil))) -> c16(A__ADD(mark(x0), recip(nil)), MARK(x0))
   MARK(add(terms(z0), recip(x1))) -> c16(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), recip(x1))) -> c16(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), recip(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), recip(x1))) -> c16(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), recip(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), recip(x1))) -> c16(A__ADD(cons(mark(z0), z1), recip(mark(x1))), MARK(cons(z0, z1)))
   MARK(add(recip(z0), recip(x1))) -> c16(A__ADD(recip(mark(z0)), recip(mark(x1))), MARK(recip(z0)))
   MARK(add(0, recip(x1))) -> c16(A__ADD(0, recip(mark(x1))), MARK(0))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0))
   MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0))
   MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0))
   MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2))))
   MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0))
   MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0))
   MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0))
   MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0))
   MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1))))
   MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0))
   MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0))
   MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0))
   MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2))))
   MARK(add(x0, cons(terms(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(sqr(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0))
   MARK(add(x0, cons(dbl(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0))
   MARK(add(x0, cons(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0))
   MARK(add(x0, cons(recip(z0), x2))) -> c16(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(s(z0), x2))) -> c16(A__ADD(mark(x0), cons(s(z0), x2)), MARK(x0))
   MARK(add(x0, cons(0, x2))) -> c16(A__ADD(mark(x0), cons(0, x2)), MARK(x0))
   MARK(add(x0, cons(nil, x2))) -> c16(A__ADD(mark(x0), cons(nil, x2)), MARK(x0))
   MARK(add(terms(z0), cons(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(terms(z0)))
   MARK(add(sqr(z0), cons(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), cons(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), cons(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), cons(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, cons(x1, x2))) -> c16(A__ADD(0, cons(mark(x1), x2)))
   MARK(add(x0, recip(terms(z0)))) -> c16(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(sqr(z0)))) -> c16(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(add(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, recip(dbl(z0)))) -> c16(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(first(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, recip(cons(z0, z1)))) -> c16(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, recip(recip(z0)))) -> c16(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(s(z0)))) -> c16(A__ADD(mark(x0), recip(s(z0))), MARK(x0))
   MARK(add(x0, recip(0))) -> c16(A__ADD(mark(x0), recip(0)), MARK(x0))
   MARK(add(x0, recip(nil))) -> c16(A__ADD(mark(x0), recip(nil)), MARK(x0))
   MARK(add(terms(z0), recip(x1))) -> c16(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), recip(x1))) -> c16(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), recip(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), recip(x1))) -> c16(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), recip(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), recip(x1))) -> c16(A__ADD(cons(mark(z0), z1), recip(mark(x1))), MARK(cons(z0, z1)))
   MARK(add(recip(z0), recip(x1))) -> c16(A__ADD(recip(mark(z0)), recip(mark(x1))), MARK(recip(z0)))
   MARK(add(0, recip(x1))) -> c16(A__ADD(0, recip(mark(x1))), MARK(0))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1


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

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

(92)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0))
   MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0))
   MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0))
   MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
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   MARK(add(0, recip(x1))) -> c16(A__ADD(0, recip(mark(x1))))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0))
   MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0))
   MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0))
   MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2))))
   MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0))
   MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0))
   MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0))
   MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0))
   MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1))))
   MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0))
   MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0))
   MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0))
   MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2))))
   MARK(add(x0, cons(terms(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(sqr(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0))
   MARK(add(x0, cons(dbl(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0))
   MARK(add(x0, cons(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0))
   MARK(add(x0, cons(recip(z0), x2))) -> c16(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(s(z0), x2))) -> c16(A__ADD(mark(x0), cons(s(z0), x2)), MARK(x0))
   MARK(add(x0, cons(0, x2))) -> c16(A__ADD(mark(x0), cons(0, x2)), MARK(x0))
   MARK(add(x0, cons(nil, x2))) -> c16(A__ADD(mark(x0), cons(nil, x2)), MARK(x0))
   MARK(add(terms(z0), cons(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(terms(z0)))
   MARK(add(sqr(z0), cons(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), cons(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), cons(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), cons(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, cons(x1, x2))) -> c16(A__ADD(0, cons(mark(x1), x2)))
   MARK(add(x0, recip(terms(z0)))) -> c16(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(sqr(z0)))) -> c16(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(add(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, recip(dbl(z0)))) -> c16(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(first(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, recip(cons(z0, z1)))) -> c16(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, recip(recip(z0)))) -> c16(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(s(z0)))) -> c16(A__ADD(mark(x0), recip(s(z0))), MARK(x0))
   MARK(add(x0, recip(0))) -> c16(A__ADD(mark(x0), recip(0)), MARK(x0))
   MARK(add(x0, recip(nil))) -> c16(A__ADD(mark(x0), recip(nil)), MARK(x0))
   MARK(add(terms(z0), recip(x1))) -> c16(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), recip(x1))) -> c16(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), recip(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), recip(x1))) -> c16(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), recip(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), recip(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), recip(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, recip(x1))) -> c16(A__ADD(0, recip(mark(x1))))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1


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

(93) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0)) by 
   MARK(add(terms(z0), s(x1))) -> c16(A__ADD(a__terms(mark(z0)), s(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), s(x1))) -> c16(A__ADD(a__sqr(mark(z0)), s(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), s(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), s(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), s(x1))) -> c16(A__ADD(a__dbl(mark(z0)), s(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), s(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), s(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), s(x1))) -> c16(A__ADD(cons(mark(z0), z1), s(x1)), MARK(cons(z0, z1)))
   MARK(add(recip(z0), s(x1))) -> c16(A__ADD(recip(mark(z0)), s(x1)), MARK(recip(z0)))
   MARK(add(s(z0), s(x1))) -> c16(A__ADD(s(z0), s(x1)), MARK(s(z0)))
   MARK(add(0, s(x1))) -> c16(A__ADD(0, s(x1)), MARK(0))
   MARK(add(nil, s(x1))) -> c16(A__ADD(nil, s(x1)), MARK(nil))

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

(94)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0))
   MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0))
   MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2))))
   MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0))
   MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0))
   MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0))
   MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0))
   MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1))))
   MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0))
   MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0))
   MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0))
   MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2))))
   MARK(add(x0, cons(terms(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(sqr(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0))
   MARK(add(x0, cons(dbl(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0))
   MARK(add(x0, cons(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0))
   MARK(add(x0, cons(recip(z0), x2))) -> c16(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(s(z0), x2))) -> c16(A__ADD(mark(x0), cons(s(z0), x2)), MARK(x0))
   MARK(add(x0, cons(0, x2))) -> c16(A__ADD(mark(x0), cons(0, x2)), MARK(x0))
   MARK(add(x0, cons(nil, x2))) -> c16(A__ADD(mark(x0), cons(nil, x2)), MARK(x0))
   MARK(add(terms(z0), cons(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(terms(z0)))
   MARK(add(sqr(z0), cons(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), cons(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), cons(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), cons(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, cons(x1, x2))) -> c16(A__ADD(0, cons(mark(x1), x2)))
   MARK(add(x0, recip(terms(z0)))) -> c16(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(sqr(z0)))) -> c16(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(add(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, recip(dbl(z0)))) -> c16(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(first(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, recip(cons(z0, z1)))) -> c16(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, recip(recip(z0)))) -> c16(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(s(z0)))) -> c16(A__ADD(mark(x0), recip(s(z0))), MARK(x0))
   MARK(add(x0, recip(0))) -> c16(A__ADD(mark(x0), recip(0)), MARK(x0))
   MARK(add(x0, recip(nil))) -> c16(A__ADD(mark(x0), recip(nil)), MARK(x0))
   MARK(add(terms(z0), recip(x1))) -> c16(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), recip(x1))) -> c16(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), recip(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), recip(x1))) -> c16(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), recip(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), recip(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), recip(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, recip(x1))) -> c16(A__ADD(0, recip(mark(x1))))
   MARK(add(terms(z0), s(x1))) -> c16(A__ADD(a__terms(mark(z0)), s(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), s(x1))) -> c16(A__ADD(a__sqr(mark(z0)), s(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), s(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), s(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), s(x1))) -> c16(A__ADD(a__dbl(mark(z0)), s(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), s(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), s(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), s(x1))) -> c16(A__ADD(cons(mark(z0), z1), s(x1)), MARK(cons(z0, z1)))
   MARK(add(recip(z0), s(x1))) -> c16(A__ADD(recip(mark(z0)), s(x1)), MARK(recip(z0)))
   MARK(add(s(z0), s(x1))) -> c16(A__ADD(s(z0), s(x1)), MARK(s(z0)))
   MARK(add(0, s(x1))) -> c16(A__ADD(0, s(x1)), MARK(0))
   MARK(add(nil, s(x1))) -> c16(A__ADD(nil, s(x1)), MARK(nil))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0))
   MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0))
   MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
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   MARK(add(sqr(z0), cons(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), cons(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), cons(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), cons(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, cons(x1, x2))) -> c16(A__ADD(0, cons(mark(x1), x2)))
   MARK(add(x0, recip(terms(z0)))) -> c16(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(sqr(z0)))) -> c16(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(add(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, recip(dbl(z0)))) -> c16(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(first(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, recip(cons(z0, z1)))) -> c16(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, recip(recip(z0)))) -> c16(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(s(z0)))) -> c16(A__ADD(mark(x0), recip(s(z0))), MARK(x0))
   MARK(add(x0, recip(0))) -> c16(A__ADD(mark(x0), recip(0)), MARK(x0))
   MARK(add(x0, recip(nil))) -> c16(A__ADD(mark(x0), recip(nil)), MARK(x0))
   MARK(add(terms(z0), recip(x1))) -> c16(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), recip(x1))) -> c16(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), recip(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), recip(x1))) -> c16(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), recip(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), recip(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), recip(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, recip(x1))) -> c16(A__ADD(0, recip(mark(x1))))
   MARK(add(terms(z0), s(x1))) -> c16(A__ADD(a__terms(mark(z0)), s(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), s(x1))) -> c16(A__ADD(a__sqr(mark(z0)), s(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), s(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), s(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), s(x1))) -> c16(A__ADD(a__dbl(mark(z0)), s(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), s(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), s(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), s(x1))) -> c16(A__ADD(cons(mark(z0), z1), s(x1)), MARK(cons(z0, z1)))
   MARK(add(recip(z0), s(x1))) -> c16(A__ADD(recip(mark(z0)), s(x1)), MARK(recip(z0)))
   MARK(add(s(z0), s(x1))) -> c16(A__ADD(s(z0), s(x1)), MARK(s(z0)))
   MARK(add(0, s(x1))) -> c16(A__ADD(0, s(x1)), MARK(0))
   MARK(add(nil, s(x1))) -> c16(A__ADD(nil, s(x1)), MARK(nil))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1


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

(95) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing nodes:
   MARK(add(s(z0), s(x1))) -> c16(A__ADD(s(z0), s(x1)), MARK(s(z0)))
   MARK(add(nil, s(x1))) -> c16(A__ADD(nil, s(x1)), MARK(nil))

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

(96)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0))
   MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0))
   MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2))))
   MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0))
   MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0))
   MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0))
   MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0))
   MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1))))
   MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0))
   MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0))
   MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0))
   MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2))))
   MARK(add(x0, cons(terms(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(sqr(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0))
   MARK(add(x0, cons(dbl(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0))
   MARK(add(x0, cons(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0))
   MARK(add(x0, cons(recip(z0), x2))) -> c16(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(s(z0), x2))) -> c16(A__ADD(mark(x0), cons(s(z0), x2)), MARK(x0))
   MARK(add(x0, cons(0, x2))) -> c16(A__ADD(mark(x0), cons(0, x2)), MARK(x0))
   MARK(add(x0, cons(nil, x2))) -> c16(A__ADD(mark(x0), cons(nil, x2)), MARK(x0))
   MARK(add(terms(z0), cons(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(terms(z0)))
   MARK(add(sqr(z0), cons(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), cons(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), cons(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), cons(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, cons(x1, x2))) -> c16(A__ADD(0, cons(mark(x1), x2)))
   MARK(add(x0, recip(terms(z0)))) -> c16(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(sqr(z0)))) -> c16(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(add(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, recip(dbl(z0)))) -> c16(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(first(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, recip(cons(z0, z1)))) -> c16(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, recip(recip(z0)))) -> c16(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(s(z0)))) -> c16(A__ADD(mark(x0), recip(s(z0))), MARK(x0))
   MARK(add(x0, recip(0))) -> c16(A__ADD(mark(x0), recip(0)), MARK(x0))
   MARK(add(x0, recip(nil))) -> c16(A__ADD(mark(x0), recip(nil)), MARK(x0))
   MARK(add(terms(z0), recip(x1))) -> c16(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), recip(x1))) -> c16(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), recip(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), recip(x1))) -> c16(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), recip(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), recip(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), recip(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, recip(x1))) -> c16(A__ADD(0, recip(mark(x1))))
   MARK(add(terms(z0), s(x1))) -> c16(A__ADD(a__terms(mark(z0)), s(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), s(x1))) -> c16(A__ADD(a__sqr(mark(z0)), s(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), s(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), s(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), s(x1))) -> c16(A__ADD(a__dbl(mark(z0)), s(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), s(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), s(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), s(x1))) -> c16(A__ADD(cons(mark(z0), z1), s(x1)), MARK(cons(z0, z1)))
   MARK(add(recip(z0), s(x1))) -> c16(A__ADD(recip(mark(z0)), s(x1)), MARK(recip(z0)))
   MARK(add(0, s(x1))) -> c16(A__ADD(0, s(x1)), MARK(0))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0))
   MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0))
   MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
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   MARK(add(dbl(z0), s(x1))) -> c16(A__ADD(a__dbl(mark(z0)), s(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), s(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), s(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), s(x1))) -> c16(A__ADD(cons(mark(z0), z1), s(x1)), MARK(cons(z0, z1)))
   MARK(add(recip(z0), s(x1))) -> c16(A__ADD(recip(mark(z0)), s(x1)), MARK(recip(z0)))
   MARK(add(0, s(x1))) -> c16(A__ADD(0, s(x1)), MARK(0))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1


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

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

(98)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0))
   MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0))
   MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2))))
   MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0))
   MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0))
   MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0))
   MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0))
   MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1))))
   MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0))
   MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0))
   MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0))
   MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2))))
   MARK(add(x0, cons(terms(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(sqr(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0))
   MARK(add(x0, cons(dbl(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0))
   MARK(add(x0, cons(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0))
   MARK(add(x0, cons(recip(z0), x2))) -> c16(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(s(z0), x2))) -> c16(A__ADD(mark(x0), cons(s(z0), x2)), MARK(x0))
   MARK(add(x0, cons(0, x2))) -> c16(A__ADD(mark(x0), cons(0, x2)), MARK(x0))
   MARK(add(x0, cons(nil, x2))) -> c16(A__ADD(mark(x0), cons(nil, x2)), MARK(x0))
   MARK(add(terms(z0), cons(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(terms(z0)))
   MARK(add(sqr(z0), cons(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), cons(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), cons(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), cons(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, cons(x1, x2))) -> c16(A__ADD(0, cons(mark(x1), x2)))
   MARK(add(x0, recip(terms(z0)))) -> c16(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(sqr(z0)))) -> c16(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(add(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, recip(dbl(z0)))) -> c16(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(first(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, recip(cons(z0, z1)))) -> c16(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, recip(recip(z0)))) -> c16(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(s(z0)))) -> c16(A__ADD(mark(x0), recip(s(z0))), MARK(x0))
   MARK(add(x0, recip(0))) -> c16(A__ADD(mark(x0), recip(0)), MARK(x0))
   MARK(add(x0, recip(nil))) -> c16(A__ADD(mark(x0), recip(nil)), MARK(x0))
   MARK(add(terms(z0), recip(x1))) -> c16(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), recip(x1))) -> c16(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), recip(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), recip(x1))) -> c16(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), recip(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), recip(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), recip(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, recip(x1))) -> c16(A__ADD(0, recip(mark(x1))))
   MARK(add(terms(z0), s(x1))) -> c16(A__ADD(a__terms(mark(z0)), s(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), s(x1))) -> c16(A__ADD(a__sqr(mark(z0)), s(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), s(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), s(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), s(x1))) -> c16(A__ADD(a__dbl(mark(z0)), s(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), s(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), s(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), s(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), s(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, s(x1))) -> c16(A__ADD(0, s(x1)))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0))
   MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0))
   MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2))))
   MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0))
   MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0))
   MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0))
   MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0))
   MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1))))
   MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0))
   MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0))
   MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0))
   MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2))))
   MARK(add(x0, cons(terms(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(sqr(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0))
   MARK(add(x0, cons(dbl(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0))
   MARK(add(x0, cons(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0))
   MARK(add(x0, cons(recip(z0), x2))) -> c16(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(s(z0), x2))) -> c16(A__ADD(mark(x0), cons(s(z0), x2)), MARK(x0))
   MARK(add(x0, cons(0, x2))) -> c16(A__ADD(mark(x0), cons(0, x2)), MARK(x0))
   MARK(add(x0, cons(nil, x2))) -> c16(A__ADD(mark(x0), cons(nil, x2)), MARK(x0))
   MARK(add(terms(z0), cons(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(terms(z0)))
   MARK(add(sqr(z0), cons(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), cons(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), cons(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), cons(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, cons(x1, x2))) -> c16(A__ADD(0, cons(mark(x1), x2)))
   MARK(add(x0, recip(terms(z0)))) -> c16(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(sqr(z0)))) -> c16(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(add(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, recip(dbl(z0)))) -> c16(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(first(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, recip(cons(z0, z1)))) -> c16(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, recip(recip(z0)))) -> c16(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(s(z0)))) -> c16(A__ADD(mark(x0), recip(s(z0))), MARK(x0))
   MARK(add(x0, recip(0))) -> c16(A__ADD(mark(x0), recip(0)), MARK(x0))
   MARK(add(x0, recip(nil))) -> c16(A__ADD(mark(x0), recip(nil)), MARK(x0))
   MARK(add(terms(z0), recip(x1))) -> c16(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), recip(x1))) -> c16(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), recip(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), recip(x1))) -> c16(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), recip(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), recip(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), recip(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, recip(x1))) -> c16(A__ADD(0, recip(mark(x1))))
   MARK(add(terms(z0), s(x1))) -> c16(A__ADD(a__terms(mark(z0)), s(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), s(x1))) -> c16(A__ADD(a__sqr(mark(z0)), s(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), s(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), s(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), s(x1))) -> c16(A__ADD(a__dbl(mark(z0)), s(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), s(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), s(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), s(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), s(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, s(x1))) -> c16(A__ADD(0, s(x1)))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1


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

(99) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0)) by 
   MARK(add(terms(z0), 0)) -> c16(A__ADD(a__terms(mark(z0)), 0), MARK(terms(z0)))
   MARK(add(sqr(z0), 0)) -> c16(A__ADD(a__sqr(mark(z0)), 0), MARK(sqr(z0)))
   MARK(add(add(z0, z1), 0)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1)))
   MARK(add(dbl(z0), 0)) -> c16(A__ADD(a__dbl(mark(z0)), 0), MARK(dbl(z0)))
   MARK(add(first(z0, z1), 0)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), 0), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), 0)) -> c16(A__ADD(cons(mark(z0), z1), 0), MARK(cons(z0, z1)))
   MARK(add(recip(z0), 0)) -> c16(A__ADD(recip(mark(z0)), 0), MARK(recip(z0)))
   MARK(add(s(z0), 0)) -> c16(A__ADD(s(z0), 0), MARK(s(z0)))
   MARK(add(0, 0)) -> c16(A__ADD(0, 0), MARK(0))
   MARK(add(nil, 0)) -> c16(A__ADD(nil, 0), MARK(nil))

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

(100)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
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   MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0))
   MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2))))
   MARK(add(x0, cons(terms(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(sqr(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0))
   MARK(add(x0, cons(dbl(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0))
   MARK(add(x0, cons(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0))
   MARK(add(x0, cons(recip(z0), x2))) -> c16(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(s(z0), x2))) -> c16(A__ADD(mark(x0), cons(s(z0), x2)), MARK(x0))
   MARK(add(x0, cons(0, x2))) -> c16(A__ADD(mark(x0), cons(0, x2)), MARK(x0))
   MARK(add(x0, cons(nil, x2))) -> c16(A__ADD(mark(x0), cons(nil, x2)), MARK(x0))
   MARK(add(terms(z0), cons(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(terms(z0)))
   MARK(add(sqr(z0), cons(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), cons(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), cons(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), cons(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, cons(x1, x2))) -> c16(A__ADD(0, cons(mark(x1), x2)))
   MARK(add(x0, recip(terms(z0)))) -> c16(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(sqr(z0)))) -> c16(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(add(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, recip(dbl(z0)))) -> c16(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(first(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, recip(cons(z0, z1)))) -> c16(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, recip(recip(z0)))) -> c16(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(s(z0)))) -> c16(A__ADD(mark(x0), recip(s(z0))), MARK(x0))
   MARK(add(x0, recip(0))) -> c16(A__ADD(mark(x0), recip(0)), MARK(x0))
   MARK(add(x0, recip(nil))) -> c16(A__ADD(mark(x0), recip(nil)), MARK(x0))
   MARK(add(terms(z0), recip(x1))) -> c16(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), recip(x1))) -> c16(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), recip(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), recip(x1))) -> c16(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), recip(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), recip(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), recip(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, recip(x1))) -> c16(A__ADD(0, recip(mark(x1))))
   MARK(add(terms(z0), s(x1))) -> c16(A__ADD(a__terms(mark(z0)), s(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), s(x1))) -> c16(A__ADD(a__sqr(mark(z0)), s(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), s(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), s(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), s(x1))) -> c16(A__ADD(a__dbl(mark(z0)), s(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), s(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), s(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), s(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), s(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, s(x1))) -> c16(A__ADD(0, s(x1)))
   MARK(add(terms(z0), 0)) -> c16(A__ADD(a__terms(mark(z0)), 0), MARK(terms(z0)))
   MARK(add(sqr(z0), 0)) -> c16(A__ADD(a__sqr(mark(z0)), 0), MARK(sqr(z0)))
   MARK(add(add(z0, z1), 0)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1)))
   MARK(add(dbl(z0), 0)) -> c16(A__ADD(a__dbl(mark(z0)), 0), MARK(dbl(z0)))
   MARK(add(first(z0, z1), 0)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), 0), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), 0)) -> c16(A__ADD(cons(mark(z0), z1), 0), MARK(cons(z0, z1)))
   MARK(add(recip(z0), 0)) -> c16(A__ADD(recip(mark(z0)), 0), MARK(recip(z0)))
   MARK(add(s(z0), 0)) -> c16(A__ADD(s(z0), 0), MARK(s(z0)))
   MARK(add(0, 0)) -> c16(A__ADD(0, 0), MARK(0))
   MARK(add(nil, 0)) -> c16(A__ADD(nil, 0), MARK(nil))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0))
   MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2))))
   MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0))
   MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0))
   MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0))
   MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0))
   MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1))))
   MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0))
   MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0))
   MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0))
   MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2))))
   MARK(add(x0, cons(terms(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(sqr(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0))
   MARK(add(x0, cons(dbl(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0))
   MARK(add(x0, cons(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0))
   MARK(add(x0, cons(recip(z0), x2))) -> c16(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(s(z0), x2))) -> c16(A__ADD(mark(x0), cons(s(z0), x2)), MARK(x0))
   MARK(add(x0, cons(0, x2))) -> c16(A__ADD(mark(x0), cons(0, x2)), MARK(x0))
   MARK(add(x0, cons(nil, x2))) -> c16(A__ADD(mark(x0), cons(nil, x2)), MARK(x0))
   MARK(add(terms(z0), cons(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(terms(z0)))
   MARK(add(sqr(z0), cons(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), cons(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), cons(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), cons(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, cons(x1, x2))) -> c16(A__ADD(0, cons(mark(x1), x2)))
   MARK(add(x0, recip(terms(z0)))) -> c16(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(sqr(z0)))) -> c16(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(add(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, recip(dbl(z0)))) -> c16(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(first(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, recip(cons(z0, z1)))) -> c16(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, recip(recip(z0)))) -> c16(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(s(z0)))) -> c16(A__ADD(mark(x0), recip(s(z0))), MARK(x0))
   MARK(add(x0, recip(0))) -> c16(A__ADD(mark(x0), recip(0)), MARK(x0))
   MARK(add(x0, recip(nil))) -> c16(A__ADD(mark(x0), recip(nil)), MARK(x0))
   MARK(add(terms(z0), recip(x1))) -> c16(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), recip(x1))) -> c16(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), recip(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), recip(x1))) -> c16(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), recip(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), recip(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), recip(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, recip(x1))) -> c16(A__ADD(0, recip(mark(x1))))
   MARK(add(terms(z0), s(x1))) -> c16(A__ADD(a__terms(mark(z0)), s(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), s(x1))) -> c16(A__ADD(a__sqr(mark(z0)), s(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), s(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), s(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), s(x1))) -> c16(A__ADD(a__dbl(mark(z0)), s(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), s(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), s(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), s(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), s(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, s(x1))) -> c16(A__ADD(0, s(x1)))
   MARK(add(terms(z0), 0)) -> c16(A__ADD(a__terms(mark(z0)), 0), MARK(terms(z0)))
   MARK(add(sqr(z0), 0)) -> c16(A__ADD(a__sqr(mark(z0)), 0), MARK(sqr(z0)))
   MARK(add(add(z0, z1), 0)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1)))
   MARK(add(dbl(z0), 0)) -> c16(A__ADD(a__dbl(mark(z0)), 0), MARK(dbl(z0)))
   MARK(add(first(z0, z1), 0)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), 0), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), 0)) -> c16(A__ADD(cons(mark(z0), z1), 0), MARK(cons(z0, z1)))
   MARK(add(recip(z0), 0)) -> c16(A__ADD(recip(mark(z0)), 0), MARK(recip(z0)))
   MARK(add(s(z0), 0)) -> c16(A__ADD(s(z0), 0), MARK(s(z0)))
   MARK(add(0, 0)) -> c16(A__ADD(0, 0), MARK(0))
   MARK(add(nil, 0)) -> c16(A__ADD(nil, 0), MARK(nil))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1


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

(101) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing nodes:
   MARK(add(nil, 0)) -> c16(A__ADD(nil, 0), MARK(nil))
   MARK(add(s(z0), 0)) -> c16(A__ADD(s(z0), 0), MARK(s(z0)))

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

(102)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0))
   MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
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   MARK(add(x0, cons(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0))
   MARK(add(x0, cons(dbl(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0))
   MARK(add(x0, cons(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0))
   MARK(add(x0, cons(recip(z0), x2))) -> c16(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(s(z0), x2))) -> c16(A__ADD(mark(x0), cons(s(z0), x2)), MARK(x0))
   MARK(add(x0, cons(0, x2))) -> c16(A__ADD(mark(x0), cons(0, x2)), MARK(x0))
   MARK(add(x0, cons(nil, x2))) -> c16(A__ADD(mark(x0), cons(nil, x2)), MARK(x0))
   MARK(add(terms(z0), cons(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(terms(z0)))
   MARK(add(sqr(z0), cons(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), cons(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), cons(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), cons(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, cons(x1, x2))) -> c16(A__ADD(0, cons(mark(x1), x2)))
   MARK(add(x0, recip(terms(z0)))) -> c16(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(sqr(z0)))) -> c16(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(add(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, recip(dbl(z0)))) -> c16(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(first(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, recip(cons(z0, z1)))) -> c16(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, recip(recip(z0)))) -> c16(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(s(z0)))) -> c16(A__ADD(mark(x0), recip(s(z0))), MARK(x0))
   MARK(add(x0, recip(0))) -> c16(A__ADD(mark(x0), recip(0)), MARK(x0))
   MARK(add(x0, recip(nil))) -> c16(A__ADD(mark(x0), recip(nil)), MARK(x0))
   MARK(add(terms(z0), recip(x1))) -> c16(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), recip(x1))) -> c16(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), recip(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), recip(x1))) -> c16(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), recip(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), recip(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), recip(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, recip(x1))) -> c16(A__ADD(0, recip(mark(x1))))
   MARK(add(terms(z0), s(x1))) -> c16(A__ADD(a__terms(mark(z0)), s(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), s(x1))) -> c16(A__ADD(a__sqr(mark(z0)), s(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), s(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), s(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), s(x1))) -> c16(A__ADD(a__dbl(mark(z0)), s(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), s(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), s(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), s(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), s(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, s(x1))) -> c16(A__ADD(0, s(x1)))
   MARK(add(terms(z0), 0)) -> c16(A__ADD(a__terms(mark(z0)), 0), MARK(terms(z0)))
   MARK(add(sqr(z0), 0)) -> c16(A__ADD(a__sqr(mark(z0)), 0), MARK(sqr(z0)))
   MARK(add(add(z0, z1), 0)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1)))
   MARK(add(dbl(z0), 0)) -> c16(A__ADD(a__dbl(mark(z0)), 0), MARK(dbl(z0)))
   MARK(add(first(z0, z1), 0)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), 0), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), 0)) -> c16(A__ADD(cons(mark(z0), z1), 0), MARK(cons(z0, z1)))
   MARK(add(recip(z0), 0)) -> c16(A__ADD(recip(mark(z0)), 0), MARK(recip(z0)))
   MARK(add(0, 0)) -> c16(A__ADD(0, 0), MARK(0))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0))
   MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2))))
   MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0))
   MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0))
   MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0))
   MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0))
   MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1))))
   MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0))
   MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0))
   MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0))
   MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2))))
   MARK(add(x0, cons(terms(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(sqr(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0))
   MARK(add(x0, cons(dbl(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0))
   MARK(add(x0, cons(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0))
   MARK(add(x0, cons(recip(z0), x2))) -> c16(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(s(z0), x2))) -> c16(A__ADD(mark(x0), cons(s(z0), x2)), MARK(x0))
   MARK(add(x0, cons(0, x2))) -> c16(A__ADD(mark(x0), cons(0, x2)), MARK(x0))
   MARK(add(x0, cons(nil, x2))) -> c16(A__ADD(mark(x0), cons(nil, x2)), MARK(x0))
   MARK(add(terms(z0), cons(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(terms(z0)))
   MARK(add(sqr(z0), cons(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), cons(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), cons(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), cons(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, cons(x1, x2))) -> c16(A__ADD(0, cons(mark(x1), x2)))
   MARK(add(x0, recip(terms(z0)))) -> c16(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(sqr(z0)))) -> c16(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(add(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, recip(dbl(z0)))) -> c16(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(first(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, recip(cons(z0, z1)))) -> c16(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, recip(recip(z0)))) -> c16(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(s(z0)))) -> c16(A__ADD(mark(x0), recip(s(z0))), MARK(x0))
   MARK(add(x0, recip(0))) -> c16(A__ADD(mark(x0), recip(0)), MARK(x0))
   MARK(add(x0, recip(nil))) -> c16(A__ADD(mark(x0), recip(nil)), MARK(x0))
   MARK(add(terms(z0), recip(x1))) -> c16(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), recip(x1))) -> c16(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), recip(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), recip(x1))) -> c16(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), recip(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), recip(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), recip(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, recip(x1))) -> c16(A__ADD(0, recip(mark(x1))))
   MARK(add(terms(z0), s(x1))) -> c16(A__ADD(a__terms(mark(z0)), s(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), s(x1))) -> c16(A__ADD(a__sqr(mark(z0)), s(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), s(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), s(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), s(x1))) -> c16(A__ADD(a__dbl(mark(z0)), s(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), s(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), s(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), s(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), s(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, s(x1))) -> c16(A__ADD(0, s(x1)))
   MARK(add(terms(z0), 0)) -> c16(A__ADD(a__terms(mark(z0)), 0), MARK(terms(z0)))
   MARK(add(sqr(z0), 0)) -> c16(A__ADD(a__sqr(mark(z0)), 0), MARK(sqr(z0)))
   MARK(add(add(z0, z1), 0)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1)))
   MARK(add(dbl(z0), 0)) -> c16(A__ADD(a__dbl(mark(z0)), 0), MARK(dbl(z0)))
   MARK(add(first(z0, z1), 0)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), 0), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), 0)) -> c16(A__ADD(cons(mark(z0), z1), 0), MARK(cons(z0, z1)))
   MARK(add(recip(z0), 0)) -> c16(A__ADD(recip(mark(z0)), 0), MARK(recip(z0)))
   MARK(add(0, 0)) -> c16(A__ADD(0, 0), MARK(0))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1


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

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

(104)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0))
   MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
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   MARK(add(x0, recip(dbl(z0)))) -> c16(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(first(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, recip(cons(z0, z1)))) -> c16(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, recip(recip(z0)))) -> c16(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(s(z0)))) -> c16(A__ADD(mark(x0), recip(s(z0))), MARK(x0))
   MARK(add(x0, recip(0))) -> c16(A__ADD(mark(x0), recip(0)), MARK(x0))
   MARK(add(x0, recip(nil))) -> c16(A__ADD(mark(x0), recip(nil)), MARK(x0))
   MARK(add(terms(z0), recip(x1))) -> c16(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), recip(x1))) -> c16(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), recip(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), recip(x1))) -> c16(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), recip(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), recip(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), recip(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, recip(x1))) -> c16(A__ADD(0, recip(mark(x1))))
   MARK(add(terms(z0), s(x1))) -> c16(A__ADD(a__terms(mark(z0)), s(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), s(x1))) -> c16(A__ADD(a__sqr(mark(z0)), s(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), s(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), s(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), s(x1))) -> c16(A__ADD(a__dbl(mark(z0)), s(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), s(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), s(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), s(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), s(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, s(x1))) -> c16(A__ADD(0, s(x1)))
   MARK(add(terms(z0), 0)) -> c16(A__ADD(a__terms(mark(z0)), 0), MARK(terms(z0)))
   MARK(add(sqr(z0), 0)) -> c16(A__ADD(a__sqr(mark(z0)), 0), MARK(sqr(z0)))
   MARK(add(add(z0, z1), 0)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1)))
   MARK(add(dbl(z0), 0)) -> c16(A__ADD(a__dbl(mark(z0)), 0), MARK(dbl(z0)))
   MARK(add(first(z0, z1), 0)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), 0), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), 0)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), 0)) -> c16(MARK(recip(z0)))
   MARK(add(0, 0)) -> c16(A__ADD(0, 0))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0))
   MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2))))
   MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0))
   MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0))
   MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0))
   MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0))
   MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1))))
   MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0))
   MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0))
   MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0))
   MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2))))
   MARK(add(x0, cons(terms(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(sqr(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0))
   MARK(add(x0, cons(dbl(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0))
   MARK(add(x0, cons(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0))
   MARK(add(x0, cons(recip(z0), x2))) -> c16(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(s(z0), x2))) -> c16(A__ADD(mark(x0), cons(s(z0), x2)), MARK(x0))
   MARK(add(x0, cons(0, x2))) -> c16(A__ADD(mark(x0), cons(0, x2)), MARK(x0))
   MARK(add(x0, cons(nil, x2))) -> c16(A__ADD(mark(x0), cons(nil, x2)), MARK(x0))
   MARK(add(terms(z0), cons(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(terms(z0)))
   MARK(add(sqr(z0), cons(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), cons(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), cons(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), cons(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, cons(x1, x2))) -> c16(A__ADD(0, cons(mark(x1), x2)))
   MARK(add(x0, recip(terms(z0)))) -> c16(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(sqr(z0)))) -> c16(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(add(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, recip(dbl(z0)))) -> c16(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(first(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, recip(cons(z0, z1)))) -> c16(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, recip(recip(z0)))) -> c16(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(s(z0)))) -> c16(A__ADD(mark(x0), recip(s(z0))), MARK(x0))
   MARK(add(x0, recip(0))) -> c16(A__ADD(mark(x0), recip(0)), MARK(x0))
   MARK(add(x0, recip(nil))) -> c16(A__ADD(mark(x0), recip(nil)), MARK(x0))
   MARK(add(terms(z0), recip(x1))) -> c16(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), recip(x1))) -> c16(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), recip(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), recip(x1))) -> c16(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), recip(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), recip(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), recip(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, recip(x1))) -> c16(A__ADD(0, recip(mark(x1))))
   MARK(add(terms(z0), s(x1))) -> c16(A__ADD(a__terms(mark(z0)), s(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), s(x1))) -> c16(A__ADD(a__sqr(mark(z0)), s(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), s(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), s(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), s(x1))) -> c16(A__ADD(a__dbl(mark(z0)), s(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), s(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), s(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), s(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), s(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, s(x1))) -> c16(A__ADD(0, s(x1)))
   MARK(add(terms(z0), 0)) -> c16(A__ADD(a__terms(mark(z0)), 0), MARK(terms(z0)))
   MARK(add(sqr(z0), 0)) -> c16(A__ADD(a__sqr(mark(z0)), 0), MARK(sqr(z0)))
   MARK(add(add(z0, z1), 0)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1)))
   MARK(add(dbl(z0), 0)) -> c16(A__ADD(a__dbl(mark(z0)), 0), MARK(dbl(z0)))
   MARK(add(first(z0, z1), 0)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), 0), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), 0)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), 0)) -> c16(MARK(recip(z0)))
   MARK(add(0, 0)) -> c16(A__ADD(0, 0))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1


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

(105) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0)) by 
   MARK(add(terms(z0), nil)) -> c16(A__ADD(a__terms(mark(z0)), nil), MARK(terms(z0)))
   MARK(add(sqr(z0), nil)) -> c16(A__ADD(a__sqr(mark(z0)), nil), MARK(sqr(z0)))
   MARK(add(add(z0, z1), nil)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), nil), MARK(add(z0, z1)))
   MARK(add(dbl(z0), nil)) -> c16(A__ADD(a__dbl(mark(z0)), nil), MARK(dbl(z0)))
   MARK(add(first(z0, z1), nil)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), nil), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), nil)) -> c16(A__ADD(cons(mark(z0), z1), nil), MARK(cons(z0, z1)))
   MARK(add(recip(z0), nil)) -> c16(A__ADD(recip(mark(z0)), nil), MARK(recip(z0)))
   MARK(add(s(z0), nil)) -> c16(A__ADD(s(z0), nil), MARK(s(z0)))
   MARK(add(0, nil)) -> c16(A__ADD(0, nil), MARK(0))
   MARK(add(nil, nil)) -> c16(A__ADD(nil, nil), MARK(nil))

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

(106)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
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   MARK(add(0, recip(x1))) -> c16(A__ADD(0, recip(mark(x1))))
   MARK(add(terms(z0), s(x1))) -> c16(A__ADD(a__terms(mark(z0)), s(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), s(x1))) -> c16(A__ADD(a__sqr(mark(z0)), s(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), s(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), s(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), s(x1))) -> c16(A__ADD(a__dbl(mark(z0)), s(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), s(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), s(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), s(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), s(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, s(x1))) -> c16(A__ADD(0, s(x1)))
   MARK(add(terms(z0), 0)) -> c16(A__ADD(a__terms(mark(z0)), 0), MARK(terms(z0)))
   MARK(add(sqr(z0), 0)) -> c16(A__ADD(a__sqr(mark(z0)), 0), MARK(sqr(z0)))
   MARK(add(add(z0, z1), 0)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1)))
   MARK(add(dbl(z0), 0)) -> c16(A__ADD(a__dbl(mark(z0)), 0), MARK(dbl(z0)))
   MARK(add(first(z0, z1), 0)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), 0), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), 0)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), 0)) -> c16(MARK(recip(z0)))
   MARK(add(0, 0)) -> c16(A__ADD(0, 0))
   MARK(add(terms(z0), nil)) -> c16(A__ADD(a__terms(mark(z0)), nil), MARK(terms(z0)))
   MARK(add(sqr(z0), nil)) -> c16(A__ADD(a__sqr(mark(z0)), nil), MARK(sqr(z0)))
   MARK(add(add(z0, z1), nil)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), nil), MARK(add(z0, z1)))
   MARK(add(dbl(z0), nil)) -> c16(A__ADD(a__dbl(mark(z0)), nil), MARK(dbl(z0)))
   MARK(add(first(z0, z1), nil)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), nil), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), nil)) -> c16(A__ADD(cons(mark(z0), z1), nil), MARK(cons(z0, z1)))
   MARK(add(recip(z0), nil)) -> c16(A__ADD(recip(mark(z0)), nil), MARK(recip(z0)))
   MARK(add(s(z0), nil)) -> c16(A__ADD(s(z0), nil), MARK(s(z0)))
   MARK(add(0, nil)) -> c16(A__ADD(0, nil), MARK(0))
   MARK(add(nil, nil)) -> c16(A__ADD(nil, nil), MARK(nil))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2))))
   MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0))
   MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0))
   MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0))
   MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0))
   MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1))))
   MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0))
   MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0))
   MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0))
   MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2))))
   MARK(add(x0, cons(terms(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(sqr(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0))
   MARK(add(x0, cons(dbl(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0))
   MARK(add(x0, cons(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0))
   MARK(add(x0, cons(recip(z0), x2))) -> c16(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(s(z0), x2))) -> c16(A__ADD(mark(x0), cons(s(z0), x2)), MARK(x0))
   MARK(add(x0, cons(0, x2))) -> c16(A__ADD(mark(x0), cons(0, x2)), MARK(x0))
   MARK(add(x0, cons(nil, x2))) -> c16(A__ADD(mark(x0), cons(nil, x2)), MARK(x0))
   MARK(add(terms(z0), cons(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(terms(z0)))
   MARK(add(sqr(z0), cons(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), cons(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), cons(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), cons(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, cons(x1, x2))) -> c16(A__ADD(0, cons(mark(x1), x2)))
   MARK(add(x0, recip(terms(z0)))) -> c16(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(sqr(z0)))) -> c16(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(add(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, recip(dbl(z0)))) -> c16(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(first(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, recip(cons(z0, z1)))) -> c16(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, recip(recip(z0)))) -> c16(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(s(z0)))) -> c16(A__ADD(mark(x0), recip(s(z0))), MARK(x0))
   MARK(add(x0, recip(0))) -> c16(A__ADD(mark(x0), recip(0)), MARK(x0))
   MARK(add(x0, recip(nil))) -> c16(A__ADD(mark(x0), recip(nil)), MARK(x0))
   MARK(add(terms(z0), recip(x1))) -> c16(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), recip(x1))) -> c16(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), recip(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), recip(x1))) -> c16(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), recip(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), recip(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), recip(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, recip(x1))) -> c16(A__ADD(0, recip(mark(x1))))
   MARK(add(terms(z0), s(x1))) -> c16(A__ADD(a__terms(mark(z0)), s(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), s(x1))) -> c16(A__ADD(a__sqr(mark(z0)), s(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), s(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), s(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), s(x1))) -> c16(A__ADD(a__dbl(mark(z0)), s(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), s(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), s(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), s(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), s(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, s(x1))) -> c16(A__ADD(0, s(x1)))
   MARK(add(terms(z0), 0)) -> c16(A__ADD(a__terms(mark(z0)), 0), MARK(terms(z0)))
   MARK(add(sqr(z0), 0)) -> c16(A__ADD(a__sqr(mark(z0)), 0), MARK(sqr(z0)))
   MARK(add(add(z0, z1), 0)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1)))
   MARK(add(dbl(z0), 0)) -> c16(A__ADD(a__dbl(mark(z0)), 0), MARK(dbl(z0)))
   MARK(add(first(z0, z1), 0)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), 0), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), 0)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), 0)) -> c16(MARK(recip(z0)))
   MARK(add(0, 0)) -> c16(A__ADD(0, 0))
   MARK(add(terms(z0), nil)) -> c16(A__ADD(a__terms(mark(z0)), nil), MARK(terms(z0)))
   MARK(add(sqr(z0), nil)) -> c16(A__ADD(a__sqr(mark(z0)), nil), MARK(sqr(z0)))
   MARK(add(add(z0, z1), nil)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), nil), MARK(add(z0, z1)))
   MARK(add(dbl(z0), nil)) -> c16(A__ADD(a__dbl(mark(z0)), nil), MARK(dbl(z0)))
   MARK(add(first(z0, z1), nil)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), nil), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), nil)) -> c16(A__ADD(cons(mark(z0), z1), nil), MARK(cons(z0, z1)))
   MARK(add(recip(z0), nil)) -> c16(A__ADD(recip(mark(z0)), nil), MARK(recip(z0)))
   MARK(add(s(z0), nil)) -> c16(A__ADD(s(z0), nil), MARK(s(z0)))
   MARK(add(0, nil)) -> c16(A__ADD(0, nil), MARK(0))
   MARK(add(nil, nil)) -> c16(A__ADD(nil, nil), MARK(nil))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1


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

(107) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing nodes:
   MARK(add(nil, nil)) -> c16(A__ADD(nil, nil), MARK(nil))
   MARK(add(s(z0), nil)) -> c16(A__ADD(s(z0), nil), MARK(s(z0)))

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

(108)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
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   MARK(add(recip(z0), s(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, s(x1))) -> c16(A__ADD(0, s(x1)))
   MARK(add(terms(z0), 0)) -> c16(A__ADD(a__terms(mark(z0)), 0), MARK(terms(z0)))
   MARK(add(sqr(z0), 0)) -> c16(A__ADD(a__sqr(mark(z0)), 0), MARK(sqr(z0)))
   MARK(add(add(z0, z1), 0)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1)))
   MARK(add(dbl(z0), 0)) -> c16(A__ADD(a__dbl(mark(z0)), 0), MARK(dbl(z0)))
   MARK(add(first(z0, z1), 0)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), 0), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), 0)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), 0)) -> c16(MARK(recip(z0)))
   MARK(add(0, 0)) -> c16(A__ADD(0, 0))
   MARK(add(terms(z0), nil)) -> c16(A__ADD(a__terms(mark(z0)), nil), MARK(terms(z0)))
   MARK(add(sqr(z0), nil)) -> c16(A__ADD(a__sqr(mark(z0)), nil), MARK(sqr(z0)))
   MARK(add(add(z0, z1), nil)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), nil), MARK(add(z0, z1)))
   MARK(add(dbl(z0), nil)) -> c16(A__ADD(a__dbl(mark(z0)), nil), MARK(dbl(z0)))
   MARK(add(first(z0, z1), nil)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), nil), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), nil)) -> c16(A__ADD(cons(mark(z0), z1), nil), MARK(cons(z0, z1)))
   MARK(add(recip(z0), nil)) -> c16(A__ADD(recip(mark(z0)), nil), MARK(recip(z0)))
   MARK(add(0, nil)) -> c16(A__ADD(0, nil), MARK(0))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2))))
   MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0))
   MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0))
   MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0))
   MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0))
   MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1))))
   MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0))
   MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0))
   MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0))
   MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2))))
   MARK(add(x0, cons(terms(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(sqr(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0))
   MARK(add(x0, cons(dbl(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0))
   MARK(add(x0, cons(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0))
   MARK(add(x0, cons(recip(z0), x2))) -> c16(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(s(z0), x2))) -> c16(A__ADD(mark(x0), cons(s(z0), x2)), MARK(x0))
   MARK(add(x0, cons(0, x2))) -> c16(A__ADD(mark(x0), cons(0, x2)), MARK(x0))
   MARK(add(x0, cons(nil, x2))) -> c16(A__ADD(mark(x0), cons(nil, x2)), MARK(x0))
   MARK(add(terms(z0), cons(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(terms(z0)))
   MARK(add(sqr(z0), cons(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), cons(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), cons(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), cons(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, cons(x1, x2))) -> c16(A__ADD(0, cons(mark(x1), x2)))
   MARK(add(x0, recip(terms(z0)))) -> c16(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(sqr(z0)))) -> c16(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(add(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, recip(dbl(z0)))) -> c16(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(first(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, recip(cons(z0, z1)))) -> c16(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, recip(recip(z0)))) -> c16(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(s(z0)))) -> c16(A__ADD(mark(x0), recip(s(z0))), MARK(x0))
   MARK(add(x0, recip(0))) -> c16(A__ADD(mark(x0), recip(0)), MARK(x0))
   MARK(add(x0, recip(nil))) -> c16(A__ADD(mark(x0), recip(nil)), MARK(x0))
   MARK(add(terms(z0), recip(x1))) -> c16(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), recip(x1))) -> c16(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), recip(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), recip(x1))) -> c16(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), recip(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), recip(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), recip(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, recip(x1))) -> c16(A__ADD(0, recip(mark(x1))))
   MARK(add(terms(z0), s(x1))) -> c16(A__ADD(a__terms(mark(z0)), s(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), s(x1))) -> c16(A__ADD(a__sqr(mark(z0)), s(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), s(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), s(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), s(x1))) -> c16(A__ADD(a__dbl(mark(z0)), s(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), s(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), s(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), s(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), s(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, s(x1))) -> c16(A__ADD(0, s(x1)))
   MARK(add(terms(z0), 0)) -> c16(A__ADD(a__terms(mark(z0)), 0), MARK(terms(z0)))
   MARK(add(sqr(z0), 0)) -> c16(A__ADD(a__sqr(mark(z0)), 0), MARK(sqr(z0)))
   MARK(add(add(z0, z1), 0)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1)))
   MARK(add(dbl(z0), 0)) -> c16(A__ADD(a__dbl(mark(z0)), 0), MARK(dbl(z0)))
   MARK(add(first(z0, z1), 0)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), 0), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), 0)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), 0)) -> c16(MARK(recip(z0)))
   MARK(add(0, 0)) -> c16(A__ADD(0, 0))
   MARK(add(terms(z0), nil)) -> c16(A__ADD(a__terms(mark(z0)), nil), MARK(terms(z0)))
   MARK(add(sqr(z0), nil)) -> c16(A__ADD(a__sqr(mark(z0)), nil), MARK(sqr(z0)))
   MARK(add(add(z0, z1), nil)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), nil), MARK(add(z0, z1)))
   MARK(add(dbl(z0), nil)) -> c16(A__ADD(a__dbl(mark(z0)), nil), MARK(dbl(z0)))
   MARK(add(first(z0, z1), nil)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), nil), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), nil)) -> c16(A__ADD(cons(mark(z0), z1), nil), MARK(cons(z0, z1)))
   MARK(add(recip(z0), nil)) -> c16(A__ADD(recip(mark(z0)), nil), MARK(recip(z0)))
   MARK(add(0, nil)) -> c16(A__ADD(0, nil), MARK(0))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1


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

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

(110)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
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   MARK(add(terms(z0), nil)) -> c16(A__ADD(a__terms(mark(z0)), nil), MARK(terms(z0)))
   MARK(add(sqr(z0), nil)) -> c16(A__ADD(a__sqr(mark(z0)), nil), MARK(sqr(z0)))
   MARK(add(add(z0, z1), nil)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), nil), MARK(add(z0, z1)))
   MARK(add(dbl(z0), nil)) -> c16(A__ADD(a__dbl(mark(z0)), nil), MARK(dbl(z0)))
   MARK(add(first(z0, z1), nil)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), nil), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), nil)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), nil)) -> c16(MARK(recip(z0)))
   MARK(add(0, nil)) -> c16(A__ADD(0, nil))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2))))
   MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0))
   MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0))
   MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0))
   MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0))
   MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1))))
   MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0))
   MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0))
   MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0))
   MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2))))
   MARK(add(x0, cons(terms(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(sqr(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0))
   MARK(add(x0, cons(dbl(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0))
   MARK(add(x0, cons(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0))
   MARK(add(x0, cons(recip(z0), x2))) -> c16(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(s(z0), x2))) -> c16(A__ADD(mark(x0), cons(s(z0), x2)), MARK(x0))
   MARK(add(x0, cons(0, x2))) -> c16(A__ADD(mark(x0), cons(0, x2)), MARK(x0))
   MARK(add(x0, cons(nil, x2))) -> c16(A__ADD(mark(x0), cons(nil, x2)), MARK(x0))
   MARK(add(terms(z0), cons(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(terms(z0)))
   MARK(add(sqr(z0), cons(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), cons(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), cons(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), cons(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, cons(x1, x2))) -> c16(A__ADD(0, cons(mark(x1), x2)))
   MARK(add(x0, recip(terms(z0)))) -> c16(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(sqr(z0)))) -> c16(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(add(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, recip(dbl(z0)))) -> c16(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(first(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, recip(cons(z0, z1)))) -> c16(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, recip(recip(z0)))) -> c16(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(s(z0)))) -> c16(A__ADD(mark(x0), recip(s(z0))), MARK(x0))
   MARK(add(x0, recip(0))) -> c16(A__ADD(mark(x0), recip(0)), MARK(x0))
   MARK(add(x0, recip(nil))) -> c16(A__ADD(mark(x0), recip(nil)), MARK(x0))
   MARK(add(terms(z0), recip(x1))) -> c16(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), recip(x1))) -> c16(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), recip(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), recip(x1))) -> c16(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), recip(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), recip(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), recip(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, recip(x1))) -> c16(A__ADD(0, recip(mark(x1))))
   MARK(add(terms(z0), s(x1))) -> c16(A__ADD(a__terms(mark(z0)), s(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), s(x1))) -> c16(A__ADD(a__sqr(mark(z0)), s(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), s(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), s(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), s(x1))) -> c16(A__ADD(a__dbl(mark(z0)), s(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), s(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), s(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), s(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), s(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, s(x1))) -> c16(A__ADD(0, s(x1)))
   MARK(add(terms(z0), 0)) -> c16(A__ADD(a__terms(mark(z0)), 0), MARK(terms(z0)))
   MARK(add(sqr(z0), 0)) -> c16(A__ADD(a__sqr(mark(z0)), 0), MARK(sqr(z0)))
   MARK(add(add(z0, z1), 0)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1)))
   MARK(add(dbl(z0), 0)) -> c16(A__ADD(a__dbl(mark(z0)), 0), MARK(dbl(z0)))
   MARK(add(first(z0, z1), 0)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), 0), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), 0)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), 0)) -> c16(MARK(recip(z0)))
   MARK(add(0, 0)) -> c16(A__ADD(0, 0))
   MARK(add(terms(z0), nil)) -> c16(A__ADD(a__terms(mark(z0)), nil), MARK(terms(z0)))
   MARK(add(sqr(z0), nil)) -> c16(A__ADD(a__sqr(mark(z0)), nil), MARK(sqr(z0)))
   MARK(add(add(z0, z1), nil)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), nil), MARK(add(z0, z1)))
   MARK(add(dbl(z0), nil)) -> c16(A__ADD(a__dbl(mark(z0)), nil), MARK(dbl(z0)))
   MARK(add(first(z0, z1), nil)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), nil), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), nil)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), nil)) -> c16(MARK(recip(z0)))
   MARK(add(0, nil)) -> c16(A__ADD(0, nil))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1


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

(111) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) by 
   MARK(add(terms(x0), terms(z0))) -> c16(A__ADD(a__terms(mark(x0)), a__terms(mark(z0))), MARK(terms(x0)))
   MARK(add(terms(x0), sqr(z0))) -> c16(A__ADD(a__terms(mark(x0)), a__sqr(mark(z0))), MARK(terms(x0)))
   MARK(add(terms(x0), add(z0, z1))) -> c16(A__ADD(a__terms(mark(x0)), a__add(mark(z0), mark(z1))), MARK(terms(x0)))
   MARK(add(terms(x0), dbl(z0))) -> c16(A__ADD(a__terms(mark(x0)), a__dbl(mark(z0))), MARK(terms(x0)))
   MARK(add(terms(x0), first(z0, z1))) -> c16(A__ADD(a__terms(mark(x0)), a__first(mark(z0), mark(z1))), MARK(terms(x0)))
   MARK(add(terms(x0), cons(z0, z1))) -> c16(A__ADD(a__terms(mark(x0)), cons(mark(z0), z1)), MARK(terms(x0)))
   MARK(add(terms(x0), recip(z0))) -> c16(A__ADD(a__terms(mark(x0)), recip(mark(z0))), MARK(terms(x0)))
   MARK(add(terms(x0), s(z0))) -> c16(A__ADD(a__terms(mark(x0)), s(z0)), MARK(terms(x0)))
   MARK(add(terms(x0), 0)) -> c16(A__ADD(a__terms(mark(x0)), 0), MARK(terms(x0)))
   MARK(add(terms(x0), nil)) -> c16(A__ADD(a__terms(mark(x0)), nil), MARK(terms(x0)))
   MARK(add(terms(x0), x1)) -> c16(A__ADD(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0)))), mark(x1)), MARK(terms(x0)))
   MARK(add(terms(x0), x1)) -> c16(A__ADD(terms(mark(x0)), mark(x1)), MARK(terms(x0)))
   MARK(add(terms(terms(z0)), x1)) -> c16(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(terms(terms(z0))))
   MARK(add(terms(sqr(z0)), x1)) -> c16(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(terms(sqr(z0))))
   MARK(add(terms(add(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(terms(add(z0, z1))))
   MARK(add(terms(dbl(z0)), x1)) -> c16(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(terms(dbl(z0))))
   MARK(add(terms(first(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(terms(first(z0, z1))))
   MARK(add(terms(cons(z0, z1)), x1)) -> c16(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(terms(cons(z0, z1))))
   MARK(add(terms(recip(z0)), x1)) -> c16(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(terms(recip(z0))))
   MARK(add(terms(s(z0)), x1)) -> c16(A__ADD(a__terms(s(z0)), mark(x1)), MARK(terms(s(z0))))
   MARK(add(terms(0), x1)) -> c16(A__ADD(a__terms(0), mark(x1)), MARK(terms(0)))
   MARK(add(terms(nil), x1)) -> c16(A__ADD(a__terms(nil), mark(x1)), MARK(terms(nil)))
   MARK(add(terms(x0), x1)) -> c16(MARK(terms(x0)))

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

(112)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
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   MARK(add(terms(z0), s(x1))) -> c16(A__ADD(a__terms(mark(z0)), s(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), s(x1))) -> c16(A__ADD(a__sqr(mark(z0)), s(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), s(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), s(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), s(x1))) -> c16(A__ADD(a__dbl(mark(z0)), s(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), s(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), s(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), s(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), s(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, s(x1))) -> c16(A__ADD(0, s(x1)))
   MARK(add(terms(z0), 0)) -> c16(A__ADD(a__terms(mark(z0)), 0), MARK(terms(z0)))
   MARK(add(sqr(z0), 0)) -> c16(A__ADD(a__sqr(mark(z0)), 0), MARK(sqr(z0)))
   MARK(add(add(z0, z1), 0)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1)))
   MARK(add(dbl(z0), 0)) -> c16(A__ADD(a__dbl(mark(z0)), 0), MARK(dbl(z0)))
   MARK(add(first(z0, z1), 0)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), 0), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), 0)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), 0)) -> c16(MARK(recip(z0)))
   MARK(add(0, 0)) -> c16(A__ADD(0, 0))
   MARK(add(terms(z0), nil)) -> c16(A__ADD(a__terms(mark(z0)), nil), MARK(terms(z0)))
   MARK(add(sqr(z0), nil)) -> c16(A__ADD(a__sqr(mark(z0)), nil), MARK(sqr(z0)))
   MARK(add(add(z0, z1), nil)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), nil), MARK(add(z0, z1)))
   MARK(add(dbl(z0), nil)) -> c16(A__ADD(a__dbl(mark(z0)), nil), MARK(dbl(z0)))
   MARK(add(first(z0, z1), nil)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), nil), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), nil)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), nil)) -> c16(MARK(recip(z0)))
   MARK(add(0, nil)) -> c16(A__ADD(0, nil))
   MARK(add(terms(x0), x1)) -> c16(A__ADD(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0)))), mark(x1)), MARK(terms(x0)))
   MARK(add(terms(x0), x1)) -> c16(A__ADD(terms(mark(x0)), mark(x1)), MARK(terms(x0)))
   MARK(add(terms(terms(z0)), x1)) -> c16(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(terms(terms(z0))))
   MARK(add(terms(sqr(z0)), x1)) -> c16(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(terms(sqr(z0))))
   MARK(add(terms(add(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(terms(add(z0, z1))))
   MARK(add(terms(dbl(z0)), x1)) -> c16(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(terms(dbl(z0))))
   MARK(add(terms(first(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(terms(first(z0, z1))))
   MARK(add(terms(cons(z0, z1)), x1)) -> c16(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(terms(cons(z0, z1))))
   MARK(add(terms(recip(z0)), x1)) -> c16(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(terms(recip(z0))))
   MARK(add(terms(s(z0)), x1)) -> c16(A__ADD(a__terms(s(z0)), mark(x1)), MARK(terms(s(z0))))
   MARK(add(terms(0), x1)) -> c16(A__ADD(a__terms(0), mark(x1)), MARK(terms(0)))
   MARK(add(terms(nil), x1)) -> c16(A__ADD(a__terms(nil), mark(x1)), MARK(terms(nil)))
   MARK(add(terms(x0), x1)) -> c16(MARK(terms(x0)))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2))))
   MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0))
   MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0))
   MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0))
   MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0))
   MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1))))
   MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0))
   MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0))
   MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0))
   MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2))))
   MARK(add(x0, cons(terms(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(sqr(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0))
   MARK(add(x0, cons(dbl(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0))
   MARK(add(x0, cons(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0))
   MARK(add(x0, cons(recip(z0), x2))) -> c16(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(s(z0), x2))) -> c16(A__ADD(mark(x0), cons(s(z0), x2)), MARK(x0))
   MARK(add(x0, cons(0, x2))) -> c16(A__ADD(mark(x0), cons(0, x2)), MARK(x0))
   MARK(add(x0, cons(nil, x2))) -> c16(A__ADD(mark(x0), cons(nil, x2)), MARK(x0))
   MARK(add(terms(z0), cons(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(terms(z0)))
   MARK(add(sqr(z0), cons(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), cons(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), cons(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), cons(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, cons(x1, x2))) -> c16(A__ADD(0, cons(mark(x1), x2)))
   MARK(add(x0, recip(terms(z0)))) -> c16(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(sqr(z0)))) -> c16(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(add(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, recip(dbl(z0)))) -> c16(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(first(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, recip(cons(z0, z1)))) -> c16(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, recip(recip(z0)))) -> c16(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(s(z0)))) -> c16(A__ADD(mark(x0), recip(s(z0))), MARK(x0))
   MARK(add(x0, recip(0))) -> c16(A__ADD(mark(x0), recip(0)), MARK(x0))
   MARK(add(x0, recip(nil))) -> c16(A__ADD(mark(x0), recip(nil)), MARK(x0))
   MARK(add(terms(z0), recip(x1))) -> c16(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), recip(x1))) -> c16(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), recip(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), recip(x1))) -> c16(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), recip(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), recip(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), recip(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, recip(x1))) -> c16(A__ADD(0, recip(mark(x1))))
   MARK(add(terms(z0), s(x1))) -> c16(A__ADD(a__terms(mark(z0)), s(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), s(x1))) -> c16(A__ADD(a__sqr(mark(z0)), s(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), s(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), s(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), s(x1))) -> c16(A__ADD(a__dbl(mark(z0)), s(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), s(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), s(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), s(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), s(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, s(x1))) -> c16(A__ADD(0, s(x1)))
   MARK(add(terms(z0), 0)) -> c16(A__ADD(a__terms(mark(z0)), 0), MARK(terms(z0)))
   MARK(add(sqr(z0), 0)) -> c16(A__ADD(a__sqr(mark(z0)), 0), MARK(sqr(z0)))
   MARK(add(add(z0, z1), 0)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1)))
   MARK(add(dbl(z0), 0)) -> c16(A__ADD(a__dbl(mark(z0)), 0), MARK(dbl(z0)))
   MARK(add(first(z0, z1), 0)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), 0), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), 0)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), 0)) -> c16(MARK(recip(z0)))
   MARK(add(0, 0)) -> c16(A__ADD(0, 0))
   MARK(add(terms(z0), nil)) -> c16(A__ADD(a__terms(mark(z0)), nil), MARK(terms(z0)))
   MARK(add(sqr(z0), nil)) -> c16(A__ADD(a__sqr(mark(z0)), nil), MARK(sqr(z0)))
   MARK(add(add(z0, z1), nil)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), nil), MARK(add(z0, z1)))
   MARK(add(dbl(z0), nil)) -> c16(A__ADD(a__dbl(mark(z0)), nil), MARK(dbl(z0)))
   MARK(add(first(z0, z1), nil)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), nil), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), nil)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), nil)) -> c16(MARK(recip(z0)))
   MARK(add(0, nil)) -> c16(A__ADD(0, nil))
   MARK(add(terms(x0), x1)) -> c16(A__ADD(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0)))), mark(x1)), MARK(terms(x0)))
   MARK(add(terms(x0), x1)) -> c16(A__ADD(terms(mark(x0)), mark(x1)), MARK(terms(x0)))
   MARK(add(terms(terms(z0)), x1)) -> c16(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(terms(terms(z0))))
   MARK(add(terms(sqr(z0)), x1)) -> c16(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(terms(sqr(z0))))
   MARK(add(terms(add(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(terms(add(z0, z1))))
   MARK(add(terms(dbl(z0)), x1)) -> c16(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(terms(dbl(z0))))
   MARK(add(terms(first(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(terms(first(z0, z1))))
   MARK(add(terms(cons(z0, z1)), x1)) -> c16(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(terms(cons(z0, z1))))
   MARK(add(terms(recip(z0)), x1)) -> c16(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(terms(recip(z0))))
   MARK(add(terms(s(z0)), x1)) -> c16(A__ADD(a__terms(s(z0)), mark(x1)), MARK(terms(s(z0))))
   MARK(add(terms(0), x1)) -> c16(A__ADD(a__terms(0), mark(x1)), MARK(terms(0)))
   MARK(add(terms(nil), x1)) -> c16(A__ADD(a__terms(nil), mark(x1)), MARK(terms(nil)))
   MARK(add(terms(x0), x1)) -> c16(MARK(terms(x0)))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1


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

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

(114)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
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   MARK(add(x0, recip(add(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, recip(dbl(z0)))) -> c16(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(first(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, recip(cons(z0, z1)))) -> c16(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, recip(recip(z0)))) -> c16(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(s(z0)))) -> c16(A__ADD(mark(x0), recip(s(z0))), MARK(x0))
   MARK(add(x0, recip(0))) -> c16(A__ADD(mark(x0), recip(0)), MARK(x0))
   MARK(add(x0, recip(nil))) -> c16(A__ADD(mark(x0), recip(nil)), MARK(x0))
   MARK(add(terms(z0), recip(x1))) -> c16(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), recip(x1))) -> c16(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), recip(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), recip(x1))) -> c16(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), recip(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), recip(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), recip(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, recip(x1))) -> c16(A__ADD(0, recip(mark(x1))))
   MARK(add(terms(z0), s(x1))) -> c16(A__ADD(a__terms(mark(z0)), s(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), s(x1))) -> c16(A__ADD(a__sqr(mark(z0)), s(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), s(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), s(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), s(x1))) -> c16(A__ADD(a__dbl(mark(z0)), s(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), s(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), s(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), s(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), s(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, s(x1))) -> c16(A__ADD(0, s(x1)))
   MARK(add(terms(z0), 0)) -> c16(A__ADD(a__terms(mark(z0)), 0), MARK(terms(z0)))
   MARK(add(sqr(z0), 0)) -> c16(A__ADD(a__sqr(mark(z0)), 0), MARK(sqr(z0)))
   MARK(add(add(z0, z1), 0)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1)))
   MARK(add(dbl(z0), 0)) -> c16(A__ADD(a__dbl(mark(z0)), 0), MARK(dbl(z0)))
   MARK(add(first(z0, z1), 0)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), 0), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), 0)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), 0)) -> c16(MARK(recip(z0)))
   MARK(add(0, 0)) -> c16(A__ADD(0, 0))
   MARK(add(terms(z0), nil)) -> c16(A__ADD(a__terms(mark(z0)), nil), MARK(terms(z0)))
   MARK(add(sqr(z0), nil)) -> c16(A__ADD(a__sqr(mark(z0)), nil), MARK(sqr(z0)))
   MARK(add(add(z0, z1), nil)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), nil), MARK(add(z0, z1)))
   MARK(add(dbl(z0), nil)) -> c16(A__ADD(a__dbl(mark(z0)), nil), MARK(dbl(z0)))
   MARK(add(first(z0, z1), nil)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), nil), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), nil)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), nil)) -> c16(MARK(recip(z0)))
   MARK(add(0, nil)) -> c16(A__ADD(0, nil))
   MARK(add(terms(terms(z0)), x1)) -> c16(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(terms(terms(z0))))
   MARK(add(terms(sqr(z0)), x1)) -> c16(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(terms(sqr(z0))))
   MARK(add(terms(add(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(terms(add(z0, z1))))
   MARK(add(terms(dbl(z0)), x1)) -> c16(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(terms(dbl(z0))))
   MARK(add(terms(first(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(terms(first(z0, z1))))
   MARK(add(terms(cons(z0, z1)), x1)) -> c16(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(terms(cons(z0, z1))))
   MARK(add(terms(recip(z0)), x1)) -> c16(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(terms(recip(z0))))
   MARK(add(terms(s(z0)), x1)) -> c16(A__ADD(a__terms(s(z0)), mark(x1)), MARK(terms(s(z0))))
   MARK(add(terms(0), x1)) -> c16(A__ADD(a__terms(0), mark(x1)), MARK(terms(0)))
   MARK(add(terms(nil), x1)) -> c16(A__ADD(a__terms(nil), mark(x1)), MARK(terms(nil)))
   MARK(add(terms(x0), x1)) -> c16(MARK(terms(x0)))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2))))
   MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0))
   MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0))
   MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0))
   MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0))
   MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1))))
   MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0))
   MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0))
   MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0))
   MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2))))
   MARK(add(x0, cons(terms(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(sqr(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0))
   MARK(add(x0, cons(dbl(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0))
   MARK(add(x0, cons(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0))
   MARK(add(x0, cons(recip(z0), x2))) -> c16(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(s(z0), x2))) -> c16(A__ADD(mark(x0), cons(s(z0), x2)), MARK(x0))
   MARK(add(x0, cons(0, x2))) -> c16(A__ADD(mark(x0), cons(0, x2)), MARK(x0))
   MARK(add(x0, cons(nil, x2))) -> c16(A__ADD(mark(x0), cons(nil, x2)), MARK(x0))
   MARK(add(terms(z0), cons(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(terms(z0)))
   MARK(add(sqr(z0), cons(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), cons(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), cons(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), cons(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, cons(x1, x2))) -> c16(A__ADD(0, cons(mark(x1), x2)))
   MARK(add(x0, recip(terms(z0)))) -> c16(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(sqr(z0)))) -> c16(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(add(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, recip(dbl(z0)))) -> c16(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(first(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, recip(cons(z0, z1)))) -> c16(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, recip(recip(z0)))) -> c16(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(s(z0)))) -> c16(A__ADD(mark(x0), recip(s(z0))), MARK(x0))
   MARK(add(x0, recip(0))) -> c16(A__ADD(mark(x0), recip(0)), MARK(x0))
   MARK(add(x0, recip(nil))) -> c16(A__ADD(mark(x0), recip(nil)), MARK(x0))
   MARK(add(terms(z0), recip(x1))) -> c16(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), recip(x1))) -> c16(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), recip(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), recip(x1))) -> c16(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), recip(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), recip(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), recip(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, recip(x1))) -> c16(A__ADD(0, recip(mark(x1))))
   MARK(add(terms(z0), s(x1))) -> c16(A__ADD(a__terms(mark(z0)), s(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), s(x1))) -> c16(A__ADD(a__sqr(mark(z0)), s(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), s(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), s(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), s(x1))) -> c16(A__ADD(a__dbl(mark(z0)), s(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), s(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), s(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), s(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), s(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, s(x1))) -> c16(A__ADD(0, s(x1)))
   MARK(add(terms(z0), 0)) -> c16(A__ADD(a__terms(mark(z0)), 0), MARK(terms(z0)))
   MARK(add(sqr(z0), 0)) -> c16(A__ADD(a__sqr(mark(z0)), 0), MARK(sqr(z0)))
   MARK(add(add(z0, z1), 0)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1)))
   MARK(add(dbl(z0), 0)) -> c16(A__ADD(a__dbl(mark(z0)), 0), MARK(dbl(z0)))
   MARK(add(first(z0, z1), 0)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), 0), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), 0)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), 0)) -> c16(MARK(recip(z0)))
   MARK(add(0, 0)) -> c16(A__ADD(0, 0))
   MARK(add(terms(z0), nil)) -> c16(A__ADD(a__terms(mark(z0)), nil), MARK(terms(z0)))
   MARK(add(sqr(z0), nil)) -> c16(A__ADD(a__sqr(mark(z0)), nil), MARK(sqr(z0)))
   MARK(add(add(z0, z1), nil)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), nil), MARK(add(z0, z1)))
   MARK(add(dbl(z0), nil)) -> c16(A__ADD(a__dbl(mark(z0)), nil), MARK(dbl(z0)))
   MARK(add(first(z0, z1), nil)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), nil), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), nil)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), nil)) -> c16(MARK(recip(z0)))
   MARK(add(0, nil)) -> c16(A__ADD(0, nil))
   MARK(add(terms(terms(z0)), x1)) -> c16(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(terms(terms(z0))))
   MARK(add(terms(sqr(z0)), x1)) -> c16(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(terms(sqr(z0))))
   MARK(add(terms(add(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(terms(add(z0, z1))))
   MARK(add(terms(dbl(z0)), x1)) -> c16(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(terms(dbl(z0))))
   MARK(add(terms(first(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(terms(first(z0, z1))))
   MARK(add(terms(cons(z0, z1)), x1)) -> c16(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(terms(cons(z0, z1))))
   MARK(add(terms(recip(z0)), x1)) -> c16(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(terms(recip(z0))))
   MARK(add(terms(s(z0)), x1)) -> c16(A__ADD(a__terms(s(z0)), mark(x1)), MARK(terms(s(z0))))
   MARK(add(terms(0), x1)) -> c16(A__ADD(a__terms(0), mark(x1)), MARK(terms(0)))
   MARK(add(terms(nil), x1)) -> c16(A__ADD(a__terms(nil), mark(x1)), MARK(terms(nil)))
   MARK(add(terms(x0), x1)) -> c16(MARK(terms(x0)))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1


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

(115) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) by 
   MARK(add(sqr(x0), terms(z0))) -> c16(A__ADD(a__sqr(mark(x0)), a__terms(mark(z0))), MARK(sqr(x0)))
   MARK(add(sqr(x0), sqr(z0))) -> c16(A__ADD(a__sqr(mark(x0)), a__sqr(mark(z0))), MARK(sqr(x0)))
   MARK(add(sqr(x0), add(z0, z1))) -> c16(A__ADD(a__sqr(mark(x0)), a__add(mark(z0), mark(z1))), MARK(sqr(x0)))
   MARK(add(sqr(x0), dbl(z0))) -> c16(A__ADD(a__sqr(mark(x0)), a__dbl(mark(z0))), MARK(sqr(x0)))
   MARK(add(sqr(x0), first(z0, z1))) -> c16(A__ADD(a__sqr(mark(x0)), a__first(mark(z0), mark(z1))), MARK(sqr(x0)))
   MARK(add(sqr(x0), cons(z0, z1))) -> c16(A__ADD(a__sqr(mark(x0)), cons(mark(z0), z1)), MARK(sqr(x0)))
   MARK(add(sqr(x0), recip(z0))) -> c16(A__ADD(a__sqr(mark(x0)), recip(mark(z0))), MARK(sqr(x0)))
   MARK(add(sqr(x0), s(z0))) -> c16(A__ADD(a__sqr(mark(x0)), s(z0)), MARK(sqr(x0)))
   MARK(add(sqr(x0), 0)) -> c16(A__ADD(a__sqr(mark(x0)), 0), MARK(sqr(x0)))
   MARK(add(sqr(x0), nil)) -> c16(A__ADD(a__sqr(mark(x0)), nil), MARK(sqr(x0)))
   MARK(add(sqr(x0), x1)) -> c16(A__ADD(sqr(mark(x0)), mark(x1)), MARK(sqr(x0)))
   MARK(add(sqr(terms(z0)), x1)) -> c16(A__ADD(a__sqr(a__terms(mark(z0))), mark(x1)), MARK(sqr(terms(z0))))
   MARK(add(sqr(sqr(z0)), x1)) -> c16(A__ADD(a__sqr(a__sqr(mark(z0))), mark(x1)), MARK(sqr(sqr(z0))))
   MARK(add(sqr(add(z0, z1)), x1)) -> c16(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), mark(x1)), MARK(sqr(add(z0, z1))))
   MARK(add(sqr(dbl(z0)), x1)) -> c16(A__ADD(a__sqr(a__dbl(mark(z0))), mark(x1)), MARK(sqr(dbl(z0))))
   MARK(add(sqr(first(z0, z1)), x1)) -> c16(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), mark(x1)), MARK(sqr(first(z0, z1))))
   MARK(add(sqr(cons(z0, z1)), x1)) -> c16(A__ADD(a__sqr(cons(mark(z0), z1)), mark(x1)), MARK(sqr(cons(z0, z1))))
   MARK(add(sqr(recip(z0)), x1)) -> c16(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(sqr(recip(z0))))
   MARK(add(sqr(s(z0)), x1)) -> c16(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(sqr(s(z0))))
   MARK(add(sqr(0), x1)) -> c16(A__ADD(a__sqr(0), mark(x1)), MARK(sqr(0)))
   MARK(add(sqr(nil), x1)) -> c16(A__ADD(a__sqr(nil), mark(x1)), MARK(sqr(nil)))
   MARK(add(sqr(x0), x1)) -> c16(MARK(sqr(x0)))

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

(116)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2))))
   MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0))
   MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0))
   MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0))
   MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0))
   MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1))))
   MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0))
   MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0))
   MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0))
   MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2))))
   MARK(add(x0, cons(terms(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(sqr(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0))
   MARK(add(x0, cons(dbl(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0))
   MARK(add(x0, cons(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0))
   MARK(add(x0, cons(recip(z0), x2))) -> c16(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(s(z0), x2))) -> c16(A__ADD(mark(x0), cons(s(z0), x2)), MARK(x0))
   MARK(add(x0, cons(0, x2))) -> c16(A__ADD(mark(x0), cons(0, x2)), MARK(x0))
   MARK(add(x0, cons(nil, x2))) -> c16(A__ADD(mark(x0), cons(nil, x2)), MARK(x0))
   MARK(add(terms(z0), cons(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(terms(z0)))
   MARK(add(sqr(z0), cons(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), cons(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), cons(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), cons(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, cons(x1, x2))) -> c16(A__ADD(0, cons(mark(x1), x2)))
   MARK(add(x0, recip(terms(z0)))) -> c16(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(sqr(z0)))) -> c16(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(add(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, recip(dbl(z0)))) -> c16(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(first(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, recip(cons(z0, z1)))) -> c16(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, recip(recip(z0)))) -> c16(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(s(z0)))) -> c16(A__ADD(mark(x0), recip(s(z0))), MARK(x0))
   MARK(add(x0, recip(0))) -> c16(A__ADD(mark(x0), recip(0)), MARK(x0))
   MARK(add(x0, recip(nil))) -> c16(A__ADD(mark(x0), recip(nil)), MARK(x0))
   MARK(add(terms(z0), recip(x1))) -> c16(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), recip(x1))) -> c16(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), recip(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), recip(x1))) -> c16(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), recip(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), recip(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), recip(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, recip(x1))) -> c16(A__ADD(0, recip(mark(x1))))
   MARK(add(terms(z0), s(x1))) -> c16(A__ADD(a__terms(mark(z0)), s(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), s(x1))) -> c16(A__ADD(a__sqr(mark(z0)), s(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), s(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), s(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), s(x1))) -> c16(A__ADD(a__dbl(mark(z0)), s(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), s(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), s(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), s(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), s(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, s(x1))) -> c16(A__ADD(0, s(x1)))
   MARK(add(terms(z0), 0)) -> c16(A__ADD(a__terms(mark(z0)), 0), MARK(terms(z0)))
   MARK(add(sqr(z0), 0)) -> c16(A__ADD(a__sqr(mark(z0)), 0), MARK(sqr(z0)))
   MARK(add(add(z0, z1), 0)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1)))
   MARK(add(dbl(z0), 0)) -> c16(A__ADD(a__dbl(mark(z0)), 0), MARK(dbl(z0)))
   MARK(add(first(z0, z1), 0)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), 0), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), 0)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), 0)) -> c16(MARK(recip(z0)))
   MARK(add(0, 0)) -> c16(A__ADD(0, 0))
   MARK(add(terms(z0), nil)) -> c16(A__ADD(a__terms(mark(z0)), nil), MARK(terms(z0)))
   MARK(add(sqr(z0), nil)) -> c16(A__ADD(a__sqr(mark(z0)), nil), MARK(sqr(z0)))
   MARK(add(add(z0, z1), nil)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), nil), MARK(add(z0, z1)))
   MARK(add(dbl(z0), nil)) -> c16(A__ADD(a__dbl(mark(z0)), nil), MARK(dbl(z0)))
   MARK(add(first(z0, z1), nil)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), nil), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), nil)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), nil)) -> c16(MARK(recip(z0)))
   MARK(add(0, nil)) -> c16(A__ADD(0, nil))
   MARK(add(terms(terms(z0)), x1)) -> c16(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(terms(terms(z0))))
   MARK(add(terms(sqr(z0)), x1)) -> c16(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(terms(sqr(z0))))
   MARK(add(terms(add(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(terms(add(z0, z1))))
   MARK(add(terms(dbl(z0)), x1)) -> c16(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(terms(dbl(z0))))
   MARK(add(terms(first(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(terms(first(z0, z1))))
   MARK(add(terms(cons(z0, z1)), x1)) -> c16(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(terms(cons(z0, z1))))
   MARK(add(terms(recip(z0)), x1)) -> c16(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(terms(recip(z0))))
   MARK(add(terms(s(z0)), x1)) -> c16(A__ADD(a__terms(s(z0)), mark(x1)), MARK(terms(s(z0))))
   MARK(add(terms(0), x1)) -> c16(A__ADD(a__terms(0), mark(x1)), MARK(terms(0)))
   MARK(add(terms(nil), x1)) -> c16(A__ADD(a__terms(nil), mark(x1)), MARK(terms(nil)))
   MARK(add(terms(x0), x1)) -> c16(MARK(terms(x0)))
   MARK(add(sqr(x0), x1)) -> c16(A__ADD(sqr(mark(x0)), mark(x1)), MARK(sqr(x0)))
   MARK(add(sqr(terms(z0)), x1)) -> c16(A__ADD(a__sqr(a__terms(mark(z0))), mark(x1)), MARK(sqr(terms(z0))))
   MARK(add(sqr(sqr(z0)), x1)) -> c16(A__ADD(a__sqr(a__sqr(mark(z0))), mark(x1)), MARK(sqr(sqr(z0))))
   MARK(add(sqr(add(z0, z1)), x1)) -> c16(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), mark(x1)), MARK(sqr(add(z0, z1))))
   MARK(add(sqr(dbl(z0)), x1)) -> c16(A__ADD(a__sqr(a__dbl(mark(z0))), mark(x1)), MARK(sqr(dbl(z0))))
   MARK(add(sqr(first(z0, z1)), x1)) -> c16(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), mark(x1)), MARK(sqr(first(z0, z1))))
   MARK(add(sqr(cons(z0, z1)), x1)) -> c16(A__ADD(a__sqr(cons(mark(z0), z1)), mark(x1)), MARK(sqr(cons(z0, z1))))
   MARK(add(sqr(recip(z0)), x1)) -> c16(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(sqr(recip(z0))))
   MARK(add(sqr(s(z0)), x1)) -> c16(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(sqr(s(z0))))
   MARK(add(sqr(0), x1)) -> c16(A__ADD(a__sqr(0), mark(x1)), MARK(sqr(0)))
   MARK(add(sqr(nil), x1)) -> c16(A__ADD(a__sqr(nil), mark(x1)), MARK(sqr(nil)))
   MARK(add(sqr(x0), x1)) -> c16(MARK(sqr(x0)))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
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   MARK(add(terms(dbl(z0)), x1)) -> c16(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(terms(dbl(z0))))
   MARK(add(terms(first(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(terms(first(z0, z1))))
   MARK(add(terms(cons(z0, z1)), x1)) -> c16(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(terms(cons(z0, z1))))
   MARK(add(terms(recip(z0)), x1)) -> c16(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(terms(recip(z0))))
   MARK(add(terms(s(z0)), x1)) -> c16(A__ADD(a__terms(s(z0)), mark(x1)), MARK(terms(s(z0))))
   MARK(add(terms(0), x1)) -> c16(A__ADD(a__terms(0), mark(x1)), MARK(terms(0)))
   MARK(add(terms(nil), x1)) -> c16(A__ADD(a__terms(nil), mark(x1)), MARK(terms(nil)))
   MARK(add(terms(x0), x1)) -> c16(MARK(terms(x0)))
   MARK(add(sqr(x0), x1)) -> c16(A__ADD(sqr(mark(x0)), mark(x1)), MARK(sqr(x0)))
   MARK(add(sqr(terms(z0)), x1)) -> c16(A__ADD(a__sqr(a__terms(mark(z0))), mark(x1)), MARK(sqr(terms(z0))))
   MARK(add(sqr(sqr(z0)), x1)) -> c16(A__ADD(a__sqr(a__sqr(mark(z0))), mark(x1)), MARK(sqr(sqr(z0))))
   MARK(add(sqr(add(z0, z1)), x1)) -> c16(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), mark(x1)), MARK(sqr(add(z0, z1))))
   MARK(add(sqr(dbl(z0)), x1)) -> c16(A__ADD(a__sqr(a__dbl(mark(z0))), mark(x1)), MARK(sqr(dbl(z0))))
   MARK(add(sqr(first(z0, z1)), x1)) -> c16(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), mark(x1)), MARK(sqr(first(z0, z1))))
   MARK(add(sqr(cons(z0, z1)), x1)) -> c16(A__ADD(a__sqr(cons(mark(z0), z1)), mark(x1)), MARK(sqr(cons(z0, z1))))
   MARK(add(sqr(recip(z0)), x1)) -> c16(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(sqr(recip(z0))))
   MARK(add(sqr(s(z0)), x1)) -> c16(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(sqr(s(z0))))
   MARK(add(sqr(0), x1)) -> c16(A__ADD(a__sqr(0), mark(x1)), MARK(sqr(0)))
   MARK(add(sqr(nil), x1)) -> c16(A__ADD(a__sqr(nil), mark(x1)), MARK(sqr(nil)))
   MARK(add(sqr(x0), x1)) -> c16(MARK(sqr(x0)))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1


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

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

(118)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2))))
   MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0))
   MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0))
   MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0))
   MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0))
   MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1))))
   MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0))
   MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0))
   MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0))
   MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2))))
   MARK(add(x0, cons(terms(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(sqr(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0))
   MARK(add(x0, cons(dbl(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0))
   MARK(add(x0, cons(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0))
   MARK(add(x0, cons(recip(z0), x2))) -> c16(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(s(z0), x2))) -> c16(A__ADD(mark(x0), cons(s(z0), x2)), MARK(x0))
   MARK(add(x0, cons(0, x2))) -> c16(A__ADD(mark(x0), cons(0, x2)), MARK(x0))
   MARK(add(x0, cons(nil, x2))) -> c16(A__ADD(mark(x0), cons(nil, x2)), MARK(x0))
   MARK(add(terms(z0), cons(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(terms(z0)))
   MARK(add(sqr(z0), cons(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), cons(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), cons(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), cons(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, cons(x1, x2))) -> c16(A__ADD(0, cons(mark(x1), x2)))
   MARK(add(x0, recip(terms(z0)))) -> c16(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(sqr(z0)))) -> c16(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(add(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, recip(dbl(z0)))) -> c16(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(first(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, recip(cons(z0, z1)))) -> c16(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, recip(recip(z0)))) -> c16(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(s(z0)))) -> c16(A__ADD(mark(x0), recip(s(z0))), MARK(x0))
   MARK(add(x0, recip(0))) -> c16(A__ADD(mark(x0), recip(0)), MARK(x0))
   MARK(add(x0, recip(nil))) -> c16(A__ADD(mark(x0), recip(nil)), MARK(x0))
   MARK(add(terms(z0), recip(x1))) -> c16(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), recip(x1))) -> c16(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), recip(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), recip(x1))) -> c16(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), recip(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), recip(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), recip(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, recip(x1))) -> c16(A__ADD(0, recip(mark(x1))))
   MARK(add(terms(z0), s(x1))) -> c16(A__ADD(a__terms(mark(z0)), s(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), s(x1))) -> c16(A__ADD(a__sqr(mark(z0)), s(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), s(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), s(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), s(x1))) -> c16(A__ADD(a__dbl(mark(z0)), s(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), s(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), s(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), s(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), s(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, s(x1))) -> c16(A__ADD(0, s(x1)))
   MARK(add(terms(z0), 0)) -> c16(A__ADD(a__terms(mark(z0)), 0), MARK(terms(z0)))
   MARK(add(sqr(z0), 0)) -> c16(A__ADD(a__sqr(mark(z0)), 0), MARK(sqr(z0)))
   MARK(add(add(z0, z1), 0)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1)))
   MARK(add(dbl(z0), 0)) -> c16(A__ADD(a__dbl(mark(z0)), 0), MARK(dbl(z0)))
   MARK(add(first(z0, z1), 0)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), 0), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), 0)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), 0)) -> c16(MARK(recip(z0)))
   MARK(add(0, 0)) -> c16(A__ADD(0, 0))
   MARK(add(terms(z0), nil)) -> c16(A__ADD(a__terms(mark(z0)), nil), MARK(terms(z0)))
   MARK(add(sqr(z0), nil)) -> c16(A__ADD(a__sqr(mark(z0)), nil), MARK(sqr(z0)))
   MARK(add(add(z0, z1), nil)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), nil), MARK(add(z0, z1)))
   MARK(add(dbl(z0), nil)) -> c16(A__ADD(a__dbl(mark(z0)), nil), MARK(dbl(z0)))
   MARK(add(first(z0, z1), nil)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), nil), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), nil)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), nil)) -> c16(MARK(recip(z0)))
   MARK(add(0, nil)) -> c16(A__ADD(0, nil))
   MARK(add(terms(terms(z0)), x1)) -> c16(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(terms(terms(z0))))
   MARK(add(terms(sqr(z0)), x1)) -> c16(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(terms(sqr(z0))))
   MARK(add(terms(add(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(terms(add(z0, z1))))
   MARK(add(terms(dbl(z0)), x1)) -> c16(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(terms(dbl(z0))))
   MARK(add(terms(first(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(terms(first(z0, z1))))
   MARK(add(terms(cons(z0, z1)), x1)) -> c16(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(terms(cons(z0, z1))))
   MARK(add(terms(recip(z0)), x1)) -> c16(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(terms(recip(z0))))
   MARK(add(terms(s(z0)), x1)) -> c16(A__ADD(a__terms(s(z0)), mark(x1)), MARK(terms(s(z0))))
   MARK(add(terms(0), x1)) -> c16(A__ADD(a__terms(0), mark(x1)), MARK(terms(0)))
   MARK(add(terms(nil), x1)) -> c16(A__ADD(a__terms(nil), mark(x1)), MARK(terms(nil)))
   MARK(add(terms(x0), x1)) -> c16(MARK(terms(x0)))
   MARK(add(sqr(terms(z0)), x1)) -> c16(A__ADD(a__sqr(a__terms(mark(z0))), mark(x1)), MARK(sqr(terms(z0))))
   MARK(add(sqr(sqr(z0)), x1)) -> c16(A__ADD(a__sqr(a__sqr(mark(z0))), mark(x1)), MARK(sqr(sqr(z0))))
   MARK(add(sqr(add(z0, z1)), x1)) -> c16(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), mark(x1)), MARK(sqr(add(z0, z1))))
   MARK(add(sqr(dbl(z0)), x1)) -> c16(A__ADD(a__sqr(a__dbl(mark(z0))), mark(x1)), MARK(sqr(dbl(z0))))
   MARK(add(sqr(first(z0, z1)), x1)) -> c16(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), mark(x1)), MARK(sqr(first(z0, z1))))
   MARK(add(sqr(cons(z0, z1)), x1)) -> c16(A__ADD(a__sqr(cons(mark(z0), z1)), mark(x1)), MARK(sqr(cons(z0, z1))))
   MARK(add(sqr(recip(z0)), x1)) -> c16(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(sqr(recip(z0))))
   MARK(add(sqr(s(z0)), x1)) -> c16(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(sqr(s(z0))))
   MARK(add(sqr(0), x1)) -> c16(A__ADD(a__sqr(0), mark(x1)), MARK(sqr(0)))
   MARK(add(sqr(nil), x1)) -> c16(A__ADD(a__sqr(nil), mark(x1)), MARK(sqr(nil)))
   MARK(add(sqr(x0), x1)) -> c16(MARK(sqr(x0)))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
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   MARK(add(x0, recip(cons(z0, z1)))) -> c16(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, recip(recip(z0)))) -> c16(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(s(z0)))) -> c16(A__ADD(mark(x0), recip(s(z0))), MARK(x0))
   MARK(add(x0, recip(0))) -> c16(A__ADD(mark(x0), recip(0)), MARK(x0))
   MARK(add(x0, recip(nil))) -> c16(A__ADD(mark(x0), recip(nil)), MARK(x0))
   MARK(add(terms(z0), recip(x1))) -> c16(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), recip(x1))) -> c16(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), recip(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), recip(x1))) -> c16(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), recip(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), recip(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), recip(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, recip(x1))) -> c16(A__ADD(0, recip(mark(x1))))
   MARK(add(terms(z0), s(x1))) -> c16(A__ADD(a__terms(mark(z0)), s(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), s(x1))) -> c16(A__ADD(a__sqr(mark(z0)), s(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), s(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), s(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), s(x1))) -> c16(A__ADD(a__dbl(mark(z0)), s(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), s(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), s(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), s(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), s(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, s(x1))) -> c16(A__ADD(0, s(x1)))
   MARK(add(terms(z0), 0)) -> c16(A__ADD(a__terms(mark(z0)), 0), MARK(terms(z0)))
   MARK(add(sqr(z0), 0)) -> c16(A__ADD(a__sqr(mark(z0)), 0), MARK(sqr(z0)))
   MARK(add(add(z0, z1), 0)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1)))
   MARK(add(dbl(z0), 0)) -> c16(A__ADD(a__dbl(mark(z0)), 0), MARK(dbl(z0)))
   MARK(add(first(z0, z1), 0)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), 0), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), 0)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), 0)) -> c16(MARK(recip(z0)))
   MARK(add(0, 0)) -> c16(A__ADD(0, 0))
   MARK(add(terms(z0), nil)) -> c16(A__ADD(a__terms(mark(z0)), nil), MARK(terms(z0)))
   MARK(add(sqr(z0), nil)) -> c16(A__ADD(a__sqr(mark(z0)), nil), MARK(sqr(z0)))
   MARK(add(add(z0, z1), nil)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), nil), MARK(add(z0, z1)))
   MARK(add(dbl(z0), nil)) -> c16(A__ADD(a__dbl(mark(z0)), nil), MARK(dbl(z0)))
   MARK(add(first(z0, z1), nil)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), nil), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), nil)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), nil)) -> c16(MARK(recip(z0)))
   MARK(add(0, nil)) -> c16(A__ADD(0, nil))
   MARK(add(terms(terms(z0)), x1)) -> c16(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(terms(terms(z0))))
   MARK(add(terms(sqr(z0)), x1)) -> c16(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(terms(sqr(z0))))
   MARK(add(terms(add(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(terms(add(z0, z1))))
   MARK(add(terms(dbl(z0)), x1)) -> c16(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(terms(dbl(z0))))
   MARK(add(terms(first(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(terms(first(z0, z1))))
   MARK(add(terms(cons(z0, z1)), x1)) -> c16(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(terms(cons(z0, z1))))
   MARK(add(terms(recip(z0)), x1)) -> c16(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(terms(recip(z0))))
   MARK(add(terms(s(z0)), x1)) -> c16(A__ADD(a__terms(s(z0)), mark(x1)), MARK(terms(s(z0))))
   MARK(add(terms(0), x1)) -> c16(A__ADD(a__terms(0), mark(x1)), MARK(terms(0)))
   MARK(add(terms(nil), x1)) -> c16(A__ADD(a__terms(nil), mark(x1)), MARK(terms(nil)))
   MARK(add(terms(x0), x1)) -> c16(MARK(terms(x0)))
   MARK(add(sqr(terms(z0)), x1)) -> c16(A__ADD(a__sqr(a__terms(mark(z0))), mark(x1)), MARK(sqr(terms(z0))))
   MARK(add(sqr(sqr(z0)), x1)) -> c16(A__ADD(a__sqr(a__sqr(mark(z0))), mark(x1)), MARK(sqr(sqr(z0))))
   MARK(add(sqr(add(z0, z1)), x1)) -> c16(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), mark(x1)), MARK(sqr(add(z0, z1))))
   MARK(add(sqr(dbl(z0)), x1)) -> c16(A__ADD(a__sqr(a__dbl(mark(z0))), mark(x1)), MARK(sqr(dbl(z0))))
   MARK(add(sqr(first(z0, z1)), x1)) -> c16(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), mark(x1)), MARK(sqr(first(z0, z1))))
   MARK(add(sqr(cons(z0, z1)), x1)) -> c16(A__ADD(a__sqr(cons(mark(z0), z1)), mark(x1)), MARK(sqr(cons(z0, z1))))
   MARK(add(sqr(recip(z0)), x1)) -> c16(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(sqr(recip(z0))))
   MARK(add(sqr(s(z0)), x1)) -> c16(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(sqr(s(z0))))
   MARK(add(sqr(0), x1)) -> c16(A__ADD(a__sqr(0), mark(x1)), MARK(sqr(0)))
   MARK(add(sqr(nil), x1)) -> c16(A__ADD(a__sqr(nil), mark(x1)), MARK(sqr(nil)))
   MARK(add(sqr(x0), x1)) -> c16(MARK(sqr(x0)))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1


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

(119) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) by 
   MARK(add(add(x0, x1), terms(z0))) -> c16(A__ADD(a__add(mark(x0), mark(x1)), a__terms(mark(z0))), MARK(add(x0, x1)))
   MARK(add(add(x0, x1), sqr(z0))) -> c16(A__ADD(a__add(mark(x0), mark(x1)), a__sqr(mark(z0))), MARK(add(x0, x1)))
   MARK(add(add(x0, x1), add(z0, z1))) -> c16(A__ADD(a__add(mark(x0), mark(x1)), a__add(mark(z0), mark(z1))), MARK(add(x0, x1)))
   MARK(add(add(x0, x1), dbl(z0))) -> c16(A__ADD(a__add(mark(x0), mark(x1)), a__dbl(mark(z0))), MARK(add(x0, x1)))
   MARK(add(add(x0, x1), first(z0, z1))) -> c16(A__ADD(a__add(mark(x0), mark(x1)), a__first(mark(z0), mark(z1))), MARK(add(x0, x1)))
   MARK(add(add(x0, x1), cons(z0, z1))) -> c16(A__ADD(a__add(mark(x0), mark(x1)), cons(mark(z0), z1)), MARK(add(x0, x1)))
   MARK(add(add(x0, x1), recip(z0))) -> c16(A__ADD(a__add(mark(x0), mark(x1)), recip(mark(z0))), MARK(add(x0, x1)))
   MARK(add(add(x0, x1), s(z0))) -> c16(A__ADD(a__add(mark(x0), mark(x1)), s(z0)), MARK(add(x0, x1)))
   MARK(add(add(x0, x1), 0)) -> c16(A__ADD(a__add(mark(x0), mark(x1)), 0), MARK(add(x0, x1)))
   MARK(add(add(x0, x1), nil)) -> c16(A__ADD(a__add(mark(x0), mark(x1)), nil), MARK(add(x0, x1)))
   MARK(add(add(x0, x1), x2)) -> c16(A__ADD(add(mark(x0), mark(x1)), mark(x2)), MARK(add(x0, x1)))
   MARK(add(add(x0, terms(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(add(x0, terms(z0))))
   MARK(add(add(x0, sqr(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(add(x0, sqr(z0))))
   MARK(add(add(x0, add(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, add(z0, z1))))
   MARK(add(add(x0, dbl(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(add(x0, dbl(z0))))
   MARK(add(add(x0, first(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, first(z0, z1))))
   MARK(add(add(x0, cons(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(add(x0, cons(z0, z1))))
   MARK(add(add(x0, recip(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), recip(mark(z0))), mark(x2)), MARK(add(x0, recip(z0))))
   MARK(add(add(x0, s(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), s(z0)), mark(x2)), MARK(add(x0, s(z0))))
   MARK(add(add(x0, 0), x2)) -> c16(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(add(x0, 0)))
   MARK(add(add(x0, nil), x2)) -> c16(A__ADD(a__add(mark(x0), nil), mark(x2)), MARK(add(x0, nil)))
   MARK(add(add(terms(z0), x1), x2)) -> c16(A__ADD(a__add(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(add(terms(z0), x1)))
   MARK(add(add(sqr(z0), x1), x2)) -> c16(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(add(sqr(z0), x1)))
   MARK(add(add(add(z0, z1), x1), x2)) -> c16(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(add(z0, z1), x1)))
   MARK(add(add(dbl(z0), x1), x2)) -> c16(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(add(dbl(z0), x1)))
   MARK(add(add(first(z0, z1), x1), x2)) -> c16(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(first(z0, z1), x1)))
   MARK(add(add(cons(z0, z1), x1), x2)) -> c16(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(add(cons(z0, z1), x1)))
   MARK(add(add(recip(z0), x1), x2)) -> c16(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(add(recip(z0), x1)))
   MARK(add(add(s(z0), x1), x2)) -> c16(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(add(s(z0), x1)))
   MARK(add(add(0, x1), x2)) -> c16(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(add(0, x1)))
   MARK(add(add(nil, x1), x2)) -> c16(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(add(nil, x1)))

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

(120)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
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   MARK(add(sqr(z0), 0)) -> c16(A__ADD(a__sqr(mark(z0)), 0), MARK(sqr(z0)))
   MARK(add(add(z0, z1), 0)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1)))
   MARK(add(dbl(z0), 0)) -> c16(A__ADD(a__dbl(mark(z0)), 0), MARK(dbl(z0)))
   MARK(add(first(z0, z1), 0)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), 0), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), 0)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), 0)) -> c16(MARK(recip(z0)))
   MARK(add(0, 0)) -> c16(A__ADD(0, 0))
   MARK(add(terms(z0), nil)) -> c16(A__ADD(a__terms(mark(z0)), nil), MARK(terms(z0)))
   MARK(add(sqr(z0), nil)) -> c16(A__ADD(a__sqr(mark(z0)), nil), MARK(sqr(z0)))
   MARK(add(add(z0, z1), nil)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), nil), MARK(add(z0, z1)))
   MARK(add(dbl(z0), nil)) -> c16(A__ADD(a__dbl(mark(z0)), nil), MARK(dbl(z0)))
   MARK(add(first(z0, z1), nil)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), nil), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), nil)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), nil)) -> c16(MARK(recip(z0)))
   MARK(add(0, nil)) -> c16(A__ADD(0, nil))
   MARK(add(terms(terms(z0)), x1)) -> c16(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(terms(terms(z0))))
   MARK(add(terms(sqr(z0)), x1)) -> c16(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(terms(sqr(z0))))
   MARK(add(terms(add(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(terms(add(z0, z1))))
   MARK(add(terms(dbl(z0)), x1)) -> c16(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(terms(dbl(z0))))
   MARK(add(terms(first(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(terms(first(z0, z1))))
   MARK(add(terms(cons(z0, z1)), x1)) -> c16(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(terms(cons(z0, z1))))
   MARK(add(terms(recip(z0)), x1)) -> c16(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(terms(recip(z0))))
   MARK(add(terms(s(z0)), x1)) -> c16(A__ADD(a__terms(s(z0)), mark(x1)), MARK(terms(s(z0))))
   MARK(add(terms(0), x1)) -> c16(A__ADD(a__terms(0), mark(x1)), MARK(terms(0)))
   MARK(add(terms(nil), x1)) -> c16(A__ADD(a__terms(nil), mark(x1)), MARK(terms(nil)))
   MARK(add(terms(x0), x1)) -> c16(MARK(terms(x0)))
   MARK(add(sqr(terms(z0)), x1)) -> c16(A__ADD(a__sqr(a__terms(mark(z0))), mark(x1)), MARK(sqr(terms(z0))))
   MARK(add(sqr(sqr(z0)), x1)) -> c16(A__ADD(a__sqr(a__sqr(mark(z0))), mark(x1)), MARK(sqr(sqr(z0))))
   MARK(add(sqr(add(z0, z1)), x1)) -> c16(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), mark(x1)), MARK(sqr(add(z0, z1))))
   MARK(add(sqr(dbl(z0)), x1)) -> c16(A__ADD(a__sqr(a__dbl(mark(z0))), mark(x1)), MARK(sqr(dbl(z0))))
   MARK(add(sqr(first(z0, z1)), x1)) -> c16(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), mark(x1)), MARK(sqr(first(z0, z1))))
   MARK(add(sqr(cons(z0, z1)), x1)) -> c16(A__ADD(a__sqr(cons(mark(z0), z1)), mark(x1)), MARK(sqr(cons(z0, z1))))
   MARK(add(sqr(recip(z0)), x1)) -> c16(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(sqr(recip(z0))))
   MARK(add(sqr(s(z0)), x1)) -> c16(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(sqr(s(z0))))
   MARK(add(sqr(0), x1)) -> c16(A__ADD(a__sqr(0), mark(x1)), MARK(sqr(0)))
   MARK(add(sqr(nil), x1)) -> c16(A__ADD(a__sqr(nil), mark(x1)), MARK(sqr(nil)))
   MARK(add(sqr(x0), x1)) -> c16(MARK(sqr(x0)))
   MARK(add(add(x0, x1), x2)) -> c16(A__ADD(add(mark(x0), mark(x1)), mark(x2)), MARK(add(x0, x1)))
   MARK(add(add(x0, terms(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(add(x0, terms(z0))))
   MARK(add(add(x0, sqr(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(add(x0, sqr(z0))))
   MARK(add(add(x0, add(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, add(z0, z1))))
   MARK(add(add(x0, dbl(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(add(x0, dbl(z0))))
   MARK(add(add(x0, first(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, first(z0, z1))))
   MARK(add(add(x0, cons(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(add(x0, cons(z0, z1))))
   MARK(add(add(x0, recip(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), recip(mark(z0))), mark(x2)), MARK(add(x0, recip(z0))))
   MARK(add(add(x0, s(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), s(z0)), mark(x2)), MARK(add(x0, s(z0))))
   MARK(add(add(x0, 0), x2)) -> c16(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(add(x0, 0)))
   MARK(add(add(x0, nil), x2)) -> c16(A__ADD(a__add(mark(x0), nil), mark(x2)), MARK(add(x0, nil)))
   MARK(add(add(terms(z0), x1), x2)) -> c16(A__ADD(a__add(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(add(terms(z0), x1)))
   MARK(add(add(sqr(z0), x1), x2)) -> c16(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(add(sqr(z0), x1)))
   MARK(add(add(add(z0, z1), x1), x2)) -> c16(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(add(z0, z1), x1)))
   MARK(add(add(dbl(z0), x1), x2)) -> c16(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(add(dbl(z0), x1)))
   MARK(add(add(first(z0, z1), x1), x2)) -> c16(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(first(z0, z1), x1)))
   MARK(add(add(cons(z0, z1), x1), x2)) -> c16(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(add(cons(z0, z1), x1)))
   MARK(add(add(recip(z0), x1), x2)) -> c16(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(add(recip(z0), x1)))
   MARK(add(add(s(z0), x1), x2)) -> c16(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(add(s(z0), x1)))
   MARK(add(add(0, x1), x2)) -> c16(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(add(0, x1)))
   MARK(add(add(nil, x1), x2)) -> c16(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(add(nil, x1)))
S tuples:
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   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
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   MARK(add(add(x0, 0), x2)) -> c16(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(add(x0, 0)))
   MARK(add(add(x0, nil), x2)) -> c16(A__ADD(a__add(mark(x0), nil), mark(x2)), MARK(add(x0, nil)))
   MARK(add(add(terms(z0), x1), x2)) -> c16(A__ADD(a__add(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(add(terms(z0), x1)))
   MARK(add(add(sqr(z0), x1), x2)) -> c16(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(add(sqr(z0), x1)))
   MARK(add(add(add(z0, z1), x1), x2)) -> c16(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(add(z0, z1), x1)))
   MARK(add(add(dbl(z0), x1), x2)) -> c16(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(add(dbl(z0), x1)))
   MARK(add(add(first(z0, z1), x1), x2)) -> c16(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(first(z0, z1), x1)))
   MARK(add(add(cons(z0, z1), x1), x2)) -> c16(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(add(cons(z0, z1), x1)))
   MARK(add(add(recip(z0), x1), x2)) -> c16(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(add(recip(z0), x1)))
   MARK(add(add(s(z0), x1), x2)) -> c16(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(add(s(z0), x1)))
   MARK(add(add(0, x1), x2)) -> c16(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(add(0, x1)))
   MARK(add(add(nil, x1), x2)) -> c16(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(add(nil, x1)))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1


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

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

(122)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2))))
   MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0))
   MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0))
   MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0))
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   MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1)))
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   MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0))
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   MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0))
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   MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0))
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   MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0))
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   MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0)))
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   MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1)))
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   MARK(add(cons(z0, z1), cons(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), cons(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, cons(x1, x2))) -> c16(A__ADD(0, cons(mark(x1), x2)))
   MARK(add(x0, recip(terms(z0)))) -> c16(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(sqr(z0)))) -> c16(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(add(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, recip(dbl(z0)))) -> c16(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(first(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, recip(cons(z0, z1)))) -> c16(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, recip(recip(z0)))) -> c16(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(s(z0)))) -> c16(A__ADD(mark(x0), recip(s(z0))), MARK(x0))
   MARK(add(x0, recip(0))) -> c16(A__ADD(mark(x0), recip(0)), MARK(x0))
   MARK(add(x0, recip(nil))) -> c16(A__ADD(mark(x0), recip(nil)), MARK(x0))
   MARK(add(terms(z0), recip(x1))) -> c16(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), recip(x1))) -> c16(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), recip(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), recip(x1))) -> c16(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), recip(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), recip(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), recip(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, recip(x1))) -> c16(A__ADD(0, recip(mark(x1))))
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   MARK(add(sqr(z0), s(x1))) -> c16(A__ADD(a__sqr(mark(z0)), s(x1)), MARK(sqr(z0)))
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   MARK(add(dbl(z0), s(x1))) -> c16(A__ADD(a__dbl(mark(z0)), s(x1)), MARK(dbl(z0)))
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   MARK(add(cons(z0, z1), s(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), s(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, s(x1))) -> c16(A__ADD(0, s(x1)))
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   MARK(add(cons(z0, z1), 0)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), 0)) -> c16(MARK(recip(z0)))
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   MARK(add(cons(z0, z1), nil)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), nil)) -> c16(MARK(recip(z0)))
   MARK(add(0, nil)) -> c16(A__ADD(0, nil))
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   MARK(add(terms(cons(z0, z1)), x1)) -> c16(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(terms(cons(z0, z1))))
   MARK(add(terms(recip(z0)), x1)) -> c16(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(terms(recip(z0))))
   MARK(add(terms(s(z0)), x1)) -> c16(A__ADD(a__terms(s(z0)), mark(x1)), MARK(terms(s(z0))))
   MARK(add(terms(0), x1)) -> c16(A__ADD(a__terms(0), mark(x1)), MARK(terms(0)))
   MARK(add(terms(nil), x1)) -> c16(A__ADD(a__terms(nil), mark(x1)), MARK(terms(nil)))
   MARK(add(terms(x0), x1)) -> c16(MARK(terms(x0)))
   MARK(add(sqr(terms(z0)), x1)) -> c16(A__ADD(a__sqr(a__terms(mark(z0))), mark(x1)), MARK(sqr(terms(z0))))
   MARK(add(sqr(sqr(z0)), x1)) -> c16(A__ADD(a__sqr(a__sqr(mark(z0))), mark(x1)), MARK(sqr(sqr(z0))))
   MARK(add(sqr(add(z0, z1)), x1)) -> c16(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), mark(x1)), MARK(sqr(add(z0, z1))))
   MARK(add(sqr(dbl(z0)), x1)) -> c16(A__ADD(a__sqr(a__dbl(mark(z0))), mark(x1)), MARK(sqr(dbl(z0))))
   MARK(add(sqr(first(z0, z1)), x1)) -> c16(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), mark(x1)), MARK(sqr(first(z0, z1))))
   MARK(add(sqr(cons(z0, z1)), x1)) -> c16(A__ADD(a__sqr(cons(mark(z0), z1)), mark(x1)), MARK(sqr(cons(z0, z1))))
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   MARK(add(sqr(s(z0)), x1)) -> c16(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(sqr(s(z0))))
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   MARK(add(sqr(nil), x1)) -> c16(A__ADD(a__sqr(nil), mark(x1)), MARK(sqr(nil)))
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   MARK(add(add(x0, recip(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), recip(mark(z0))), mark(x2)), MARK(add(x0, recip(z0))))
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   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
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   MARK(add(x0, cons(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0))
   MARK(add(x0, cons(recip(z0), x2))) -> c16(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(s(z0), x2))) -> c16(A__ADD(mark(x0), cons(s(z0), x2)), MARK(x0))
   MARK(add(x0, cons(0, x2))) -> c16(A__ADD(mark(x0), cons(0, x2)), MARK(x0))
   MARK(add(x0, cons(nil, x2))) -> c16(A__ADD(mark(x0), cons(nil, x2)), MARK(x0))
   MARK(add(terms(z0), cons(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(terms(z0)))
   MARK(add(sqr(z0), cons(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), cons(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), cons(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), cons(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, cons(x1, x2))) -> c16(A__ADD(0, cons(mark(x1), x2)))
   MARK(add(x0, recip(terms(z0)))) -> c16(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(sqr(z0)))) -> c16(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(add(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, recip(dbl(z0)))) -> c16(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(first(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, recip(cons(z0, z1)))) -> c16(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, recip(recip(z0)))) -> c16(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(s(z0)))) -> c16(A__ADD(mark(x0), recip(s(z0))), MARK(x0))
   MARK(add(x0, recip(0))) -> c16(A__ADD(mark(x0), recip(0)), MARK(x0))
   MARK(add(x0, recip(nil))) -> c16(A__ADD(mark(x0), recip(nil)), MARK(x0))
   MARK(add(terms(z0), recip(x1))) -> c16(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), recip(x1))) -> c16(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), recip(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), recip(x1))) -> c16(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), recip(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), recip(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), recip(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, recip(x1))) -> c16(A__ADD(0, recip(mark(x1))))
   MARK(add(terms(z0), s(x1))) -> c16(A__ADD(a__terms(mark(z0)), s(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), s(x1))) -> c16(A__ADD(a__sqr(mark(z0)), s(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), s(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), s(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), s(x1))) -> c16(A__ADD(a__dbl(mark(z0)), s(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), s(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), s(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), s(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), s(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, s(x1))) -> c16(A__ADD(0, s(x1)))
   MARK(add(terms(z0), 0)) -> c16(A__ADD(a__terms(mark(z0)), 0), MARK(terms(z0)))
   MARK(add(sqr(z0), 0)) -> c16(A__ADD(a__sqr(mark(z0)), 0), MARK(sqr(z0)))
   MARK(add(add(z0, z1), 0)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1)))
   MARK(add(dbl(z0), 0)) -> c16(A__ADD(a__dbl(mark(z0)), 0), MARK(dbl(z0)))
   MARK(add(first(z0, z1), 0)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), 0), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), 0)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), 0)) -> c16(MARK(recip(z0)))
   MARK(add(0, 0)) -> c16(A__ADD(0, 0))
   MARK(add(terms(z0), nil)) -> c16(A__ADD(a__terms(mark(z0)), nil), MARK(terms(z0)))
   MARK(add(sqr(z0), nil)) -> c16(A__ADD(a__sqr(mark(z0)), nil), MARK(sqr(z0)))
   MARK(add(add(z0, z1), nil)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), nil), MARK(add(z0, z1)))
   MARK(add(dbl(z0), nil)) -> c16(A__ADD(a__dbl(mark(z0)), nil), MARK(dbl(z0)))
   MARK(add(first(z0, z1), nil)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), nil), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), nil)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), nil)) -> c16(MARK(recip(z0)))
   MARK(add(0, nil)) -> c16(A__ADD(0, nil))
   MARK(add(terms(terms(z0)), x1)) -> c16(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(terms(terms(z0))))
   MARK(add(terms(sqr(z0)), x1)) -> c16(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(terms(sqr(z0))))
   MARK(add(terms(add(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(terms(add(z0, z1))))
   MARK(add(terms(dbl(z0)), x1)) -> c16(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(terms(dbl(z0))))
   MARK(add(terms(first(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(terms(first(z0, z1))))
   MARK(add(terms(cons(z0, z1)), x1)) -> c16(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(terms(cons(z0, z1))))
   MARK(add(terms(recip(z0)), x1)) -> c16(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(terms(recip(z0))))
   MARK(add(terms(s(z0)), x1)) -> c16(A__ADD(a__terms(s(z0)), mark(x1)), MARK(terms(s(z0))))
   MARK(add(terms(0), x1)) -> c16(A__ADD(a__terms(0), mark(x1)), MARK(terms(0)))
   MARK(add(terms(nil), x1)) -> c16(A__ADD(a__terms(nil), mark(x1)), MARK(terms(nil)))
   MARK(add(terms(x0), x1)) -> c16(MARK(terms(x0)))
   MARK(add(sqr(terms(z0)), x1)) -> c16(A__ADD(a__sqr(a__terms(mark(z0))), mark(x1)), MARK(sqr(terms(z0))))
   MARK(add(sqr(sqr(z0)), x1)) -> c16(A__ADD(a__sqr(a__sqr(mark(z0))), mark(x1)), MARK(sqr(sqr(z0))))
   MARK(add(sqr(add(z0, z1)), x1)) -> c16(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), mark(x1)), MARK(sqr(add(z0, z1))))
   MARK(add(sqr(dbl(z0)), x1)) -> c16(A__ADD(a__sqr(a__dbl(mark(z0))), mark(x1)), MARK(sqr(dbl(z0))))
   MARK(add(sqr(first(z0, z1)), x1)) -> c16(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), mark(x1)), MARK(sqr(first(z0, z1))))
   MARK(add(sqr(cons(z0, z1)), x1)) -> c16(A__ADD(a__sqr(cons(mark(z0), z1)), mark(x1)), MARK(sqr(cons(z0, z1))))
   MARK(add(sqr(recip(z0)), x1)) -> c16(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(sqr(recip(z0))))
   MARK(add(sqr(s(z0)), x1)) -> c16(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(sqr(s(z0))))
   MARK(add(sqr(0), x1)) -> c16(A__ADD(a__sqr(0), mark(x1)), MARK(sqr(0)))
   MARK(add(sqr(nil), x1)) -> c16(A__ADD(a__sqr(nil), mark(x1)), MARK(sqr(nil)))
   MARK(add(sqr(x0), x1)) -> c16(MARK(sqr(x0)))
   MARK(add(add(x0, terms(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(add(x0, terms(z0))))
   MARK(add(add(x0, sqr(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(add(x0, sqr(z0))))
   MARK(add(add(x0, add(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, add(z0, z1))))
   MARK(add(add(x0, dbl(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(add(x0, dbl(z0))))
   MARK(add(add(x0, first(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, first(z0, z1))))
   MARK(add(add(x0, cons(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(add(x0, cons(z0, z1))))
   MARK(add(add(x0, recip(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), recip(mark(z0))), mark(x2)), MARK(add(x0, recip(z0))))
   MARK(add(add(x0, s(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), s(z0)), mark(x2)), MARK(add(x0, s(z0))))
   MARK(add(add(x0, 0), x2)) -> c16(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(add(x0, 0)))
   MARK(add(add(x0, nil), x2)) -> c16(A__ADD(a__add(mark(x0), nil), mark(x2)), MARK(add(x0, nil)))
   MARK(add(add(terms(z0), x1), x2)) -> c16(A__ADD(a__add(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(add(terms(z0), x1)))
   MARK(add(add(sqr(z0), x1), x2)) -> c16(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(add(sqr(z0), x1)))
   MARK(add(add(add(z0, z1), x1), x2)) -> c16(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(add(z0, z1), x1)))
   MARK(add(add(dbl(z0), x1), x2)) -> c16(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(add(dbl(z0), x1)))
   MARK(add(add(first(z0, z1), x1), x2)) -> c16(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(first(z0, z1), x1)))
   MARK(add(add(cons(z0, z1), x1), x2)) -> c16(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(add(cons(z0, z1), x1)))
   MARK(add(add(recip(z0), x1), x2)) -> c16(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(add(recip(z0), x1)))
   MARK(add(add(s(z0), x1), x2)) -> c16(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(add(s(z0), x1)))
   MARK(add(add(0, x1), x2)) -> c16(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(add(0, x1)))
   MARK(add(add(nil, x1), x2)) -> c16(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(add(nil, x1)))
   MARK(add(add(x0, x1), x2)) -> c16(MARK(add(x0, x1)))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1


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

(123) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) by 
   MARK(add(dbl(x0), terms(z0))) -> c16(A__ADD(a__dbl(mark(x0)), a__terms(mark(z0))), MARK(dbl(x0)))
   MARK(add(dbl(x0), sqr(z0))) -> c16(A__ADD(a__dbl(mark(x0)), a__sqr(mark(z0))), MARK(dbl(x0)))
   MARK(add(dbl(x0), add(z0, z1))) -> c16(A__ADD(a__dbl(mark(x0)), a__add(mark(z0), mark(z1))), MARK(dbl(x0)))
   MARK(add(dbl(x0), dbl(z0))) -> c16(A__ADD(a__dbl(mark(x0)), a__dbl(mark(z0))), MARK(dbl(x0)))
   MARK(add(dbl(x0), first(z0, z1))) -> c16(A__ADD(a__dbl(mark(x0)), a__first(mark(z0), mark(z1))), MARK(dbl(x0)))
   MARK(add(dbl(x0), cons(z0, z1))) -> c16(A__ADD(a__dbl(mark(x0)), cons(mark(z0), z1)), MARK(dbl(x0)))
   MARK(add(dbl(x0), recip(z0))) -> c16(A__ADD(a__dbl(mark(x0)), recip(mark(z0))), MARK(dbl(x0)))
   MARK(add(dbl(x0), s(z0))) -> c16(A__ADD(a__dbl(mark(x0)), s(z0)), MARK(dbl(x0)))
   MARK(add(dbl(x0), 0)) -> c16(A__ADD(a__dbl(mark(x0)), 0), MARK(dbl(x0)))
   MARK(add(dbl(x0), nil)) -> c16(A__ADD(a__dbl(mark(x0)), nil), MARK(dbl(x0)))
   MARK(add(dbl(x0), x1)) -> c16(A__ADD(dbl(mark(x0)), mark(x1)), MARK(dbl(x0)))
   MARK(add(dbl(terms(z0)), x1)) -> c16(A__ADD(a__dbl(a__terms(mark(z0))), mark(x1)), MARK(dbl(terms(z0))))
   MARK(add(dbl(sqr(z0)), x1)) -> c16(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(dbl(sqr(z0))))
   MARK(add(dbl(add(z0, z1)), x1)) -> c16(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(dbl(add(z0, z1))))
   MARK(add(dbl(dbl(z0)), x1)) -> c16(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(dbl(dbl(z0))))
   MARK(add(dbl(first(z0, z1)), x1)) -> c16(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(dbl(first(z0, z1))))
   MARK(add(dbl(cons(z0, z1)), x1)) -> c16(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(dbl(cons(z0, z1))))
   MARK(add(dbl(recip(z0)), x1)) -> c16(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(dbl(recip(z0))))
   MARK(add(dbl(s(z0)), x1)) -> c16(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(dbl(s(z0))))
   MARK(add(dbl(0), x1)) -> c16(A__ADD(a__dbl(0), mark(x1)), MARK(dbl(0)))
   MARK(add(dbl(nil), x1)) -> c16(A__ADD(a__dbl(nil), mark(x1)), MARK(dbl(nil)))
   MARK(add(dbl(x0), x1)) -> c16(MARK(dbl(x0)))

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

(124)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
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   MARK(add(first(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), cons(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), cons(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, cons(x1, x2))) -> c16(A__ADD(0, cons(mark(x1), x2)))
   MARK(add(x0, recip(terms(z0)))) -> c16(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(sqr(z0)))) -> c16(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(add(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, recip(dbl(z0)))) -> c16(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(first(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, recip(cons(z0, z1)))) -> c16(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, recip(recip(z0)))) -> c16(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, recip(s(z0)))) -> c16(A__ADD(mark(x0), recip(s(z0))), MARK(x0))
   MARK(add(x0, recip(0))) -> c16(A__ADD(mark(x0), recip(0)), MARK(x0))
   MARK(add(x0, recip(nil))) -> c16(A__ADD(mark(x0), recip(nil)), MARK(x0))
   MARK(add(terms(z0), recip(x1))) -> c16(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), recip(x1))) -> c16(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), recip(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), recip(x1))) -> c16(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), recip(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), recip(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), recip(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, recip(x1))) -> c16(A__ADD(0, recip(mark(x1))))
   MARK(add(terms(z0), s(x1))) -> c16(A__ADD(a__terms(mark(z0)), s(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), s(x1))) -> c16(A__ADD(a__sqr(mark(z0)), s(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), s(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), s(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), s(x1))) -> c16(A__ADD(a__dbl(mark(z0)), s(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), s(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), s(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), s(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), s(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, s(x1))) -> c16(A__ADD(0, s(x1)))
   MARK(add(terms(z0), 0)) -> c16(A__ADD(a__terms(mark(z0)), 0), MARK(terms(z0)))
   MARK(add(sqr(z0), 0)) -> c16(A__ADD(a__sqr(mark(z0)), 0), MARK(sqr(z0)))
   MARK(add(add(z0, z1), 0)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1)))
   MARK(add(dbl(z0), 0)) -> c16(A__ADD(a__dbl(mark(z0)), 0), MARK(dbl(z0)))
   MARK(add(first(z0, z1), 0)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), 0), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), 0)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), 0)) -> c16(MARK(recip(z0)))
   MARK(add(0, 0)) -> c16(A__ADD(0, 0))
   MARK(add(terms(z0), nil)) -> c16(A__ADD(a__terms(mark(z0)), nil), MARK(terms(z0)))
   MARK(add(sqr(z0), nil)) -> c16(A__ADD(a__sqr(mark(z0)), nil), MARK(sqr(z0)))
   MARK(add(add(z0, z1), nil)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), nil), MARK(add(z0, z1)))
   MARK(add(dbl(z0), nil)) -> c16(A__ADD(a__dbl(mark(z0)), nil), MARK(dbl(z0)))
   MARK(add(first(z0, z1), nil)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), nil), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), nil)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), nil)) -> c16(MARK(recip(z0)))
   MARK(add(0, nil)) -> c16(A__ADD(0, nil))
   MARK(add(terms(terms(z0)), x1)) -> c16(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(terms(terms(z0))))
   MARK(add(terms(sqr(z0)), x1)) -> c16(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(terms(sqr(z0))))
   MARK(add(terms(add(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(terms(add(z0, z1))))
   MARK(add(terms(dbl(z0)), x1)) -> c16(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(terms(dbl(z0))))
   MARK(add(terms(first(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(terms(first(z0, z1))))
   MARK(add(terms(cons(z0, z1)), x1)) -> c16(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(terms(cons(z0, z1))))
   MARK(add(terms(recip(z0)), x1)) -> c16(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(terms(recip(z0))))
   MARK(add(terms(s(z0)), x1)) -> c16(A__ADD(a__terms(s(z0)), mark(x1)), MARK(terms(s(z0))))
   MARK(add(terms(0), x1)) -> c16(A__ADD(a__terms(0), mark(x1)), MARK(terms(0)))
   MARK(add(terms(nil), x1)) -> c16(A__ADD(a__terms(nil), mark(x1)), MARK(terms(nil)))
   MARK(add(terms(x0), x1)) -> c16(MARK(terms(x0)))
   MARK(add(sqr(terms(z0)), x1)) -> c16(A__ADD(a__sqr(a__terms(mark(z0))), mark(x1)), MARK(sqr(terms(z0))))
   MARK(add(sqr(sqr(z0)), x1)) -> c16(A__ADD(a__sqr(a__sqr(mark(z0))), mark(x1)), MARK(sqr(sqr(z0))))
   MARK(add(sqr(add(z0, z1)), x1)) -> c16(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), mark(x1)), MARK(sqr(add(z0, z1))))
   MARK(add(sqr(dbl(z0)), x1)) -> c16(A__ADD(a__sqr(a__dbl(mark(z0))), mark(x1)), MARK(sqr(dbl(z0))))
   MARK(add(sqr(first(z0, z1)), x1)) -> c16(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), mark(x1)), MARK(sqr(first(z0, z1))))
   MARK(add(sqr(cons(z0, z1)), x1)) -> c16(A__ADD(a__sqr(cons(mark(z0), z1)), mark(x1)), MARK(sqr(cons(z0, z1))))
   MARK(add(sqr(recip(z0)), x1)) -> c16(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(sqr(recip(z0))))
   MARK(add(sqr(s(z0)), x1)) -> c16(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(sqr(s(z0))))
   MARK(add(sqr(0), x1)) -> c16(A__ADD(a__sqr(0), mark(x1)), MARK(sqr(0)))
   MARK(add(sqr(nil), x1)) -> c16(A__ADD(a__sqr(nil), mark(x1)), MARK(sqr(nil)))
   MARK(add(sqr(x0), x1)) -> c16(MARK(sqr(x0)))
   MARK(add(add(x0, terms(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(add(x0, terms(z0))))
   MARK(add(add(x0, sqr(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(add(x0, sqr(z0))))
   MARK(add(add(x0, add(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, add(z0, z1))))
   MARK(add(add(x0, dbl(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(add(x0, dbl(z0))))
   MARK(add(add(x0, first(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, first(z0, z1))))
   MARK(add(add(x0, cons(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(add(x0, cons(z0, z1))))
   MARK(add(add(x0, recip(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), recip(mark(z0))), mark(x2)), MARK(add(x0, recip(z0))))
   MARK(add(add(x0, s(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), s(z0)), mark(x2)), MARK(add(x0, s(z0))))
   MARK(add(add(x0, 0), x2)) -> c16(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(add(x0, 0)))
   MARK(add(add(x0, nil), x2)) -> c16(A__ADD(a__add(mark(x0), nil), mark(x2)), MARK(add(x0, nil)))
   MARK(add(add(terms(z0), x1), x2)) -> c16(A__ADD(a__add(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(add(terms(z0), x1)))
   MARK(add(add(sqr(z0), x1), x2)) -> c16(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(add(sqr(z0), x1)))
   MARK(add(add(add(z0, z1), x1), x2)) -> c16(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(add(z0, z1), x1)))
   MARK(add(add(dbl(z0), x1), x2)) -> c16(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(add(dbl(z0), x1)))
   MARK(add(add(first(z0, z1), x1), x2)) -> c16(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(first(z0, z1), x1)))
   MARK(add(add(cons(z0, z1), x1), x2)) -> c16(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(add(cons(z0, z1), x1)))
   MARK(add(add(recip(z0), x1), x2)) -> c16(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(add(recip(z0), x1)))
   MARK(add(add(s(z0), x1), x2)) -> c16(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(add(s(z0), x1)))
   MARK(add(add(0, x1), x2)) -> c16(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(add(0, x1)))
   MARK(add(add(nil, x1), x2)) -> c16(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(add(nil, x1)))
   MARK(add(add(x0, x1), x2)) -> c16(MARK(add(x0, x1)))
   MARK(add(dbl(x0), x1)) -> c16(A__ADD(dbl(mark(x0)), mark(x1)), MARK(dbl(x0)))
   MARK(add(dbl(terms(z0)), x1)) -> c16(A__ADD(a__dbl(a__terms(mark(z0))), mark(x1)), MARK(dbl(terms(z0))))
   MARK(add(dbl(sqr(z0)), x1)) -> c16(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(dbl(sqr(z0))))
   MARK(add(dbl(add(z0, z1)), x1)) -> c16(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(dbl(add(z0, z1))))
   MARK(add(dbl(dbl(z0)), x1)) -> c16(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(dbl(dbl(z0))))
   MARK(add(dbl(first(z0, z1)), x1)) -> c16(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(dbl(first(z0, z1))))
   MARK(add(dbl(cons(z0, z1)), x1)) -> c16(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(dbl(cons(z0, z1))))
   MARK(add(dbl(recip(z0)), x1)) -> c16(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(dbl(recip(z0))))
   MARK(add(dbl(s(z0)), x1)) -> c16(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(dbl(s(z0))))
   MARK(add(dbl(0), x1)) -> c16(A__ADD(a__dbl(0), mark(x1)), MARK(dbl(0)))
   MARK(add(dbl(nil), x1)) -> c16(A__ADD(a__dbl(nil), mark(x1)), MARK(dbl(nil)))
   MARK(add(dbl(x0), x1)) -> c16(MARK(dbl(x0)))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
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   MARK(add(sqr(z0), nil)) -> c16(A__ADD(a__sqr(mark(z0)), nil), MARK(sqr(z0)))
   MARK(add(add(z0, z1), nil)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), nil), MARK(add(z0, z1)))
   MARK(add(dbl(z0), nil)) -> c16(A__ADD(a__dbl(mark(z0)), nil), MARK(dbl(z0)))
   MARK(add(first(z0, z1), nil)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), nil), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), nil)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), nil)) -> c16(MARK(recip(z0)))
   MARK(add(0, nil)) -> c16(A__ADD(0, nil))
   MARK(add(terms(terms(z0)), x1)) -> c16(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(terms(terms(z0))))
   MARK(add(terms(sqr(z0)), x1)) -> c16(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(terms(sqr(z0))))
   MARK(add(terms(add(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(terms(add(z0, z1))))
   MARK(add(terms(dbl(z0)), x1)) -> c16(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(terms(dbl(z0))))
   MARK(add(terms(first(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(terms(first(z0, z1))))
   MARK(add(terms(cons(z0, z1)), x1)) -> c16(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(terms(cons(z0, z1))))
   MARK(add(terms(recip(z0)), x1)) -> c16(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(terms(recip(z0))))
   MARK(add(terms(s(z0)), x1)) -> c16(A__ADD(a__terms(s(z0)), mark(x1)), MARK(terms(s(z0))))
   MARK(add(terms(0), x1)) -> c16(A__ADD(a__terms(0), mark(x1)), MARK(terms(0)))
   MARK(add(terms(nil), x1)) -> c16(A__ADD(a__terms(nil), mark(x1)), MARK(terms(nil)))
   MARK(add(terms(x0), x1)) -> c16(MARK(terms(x0)))
   MARK(add(sqr(terms(z0)), x1)) -> c16(A__ADD(a__sqr(a__terms(mark(z0))), mark(x1)), MARK(sqr(terms(z0))))
   MARK(add(sqr(sqr(z0)), x1)) -> c16(A__ADD(a__sqr(a__sqr(mark(z0))), mark(x1)), MARK(sqr(sqr(z0))))
   MARK(add(sqr(add(z0, z1)), x1)) -> c16(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), mark(x1)), MARK(sqr(add(z0, z1))))
   MARK(add(sqr(dbl(z0)), x1)) -> c16(A__ADD(a__sqr(a__dbl(mark(z0))), mark(x1)), MARK(sqr(dbl(z0))))
   MARK(add(sqr(first(z0, z1)), x1)) -> c16(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), mark(x1)), MARK(sqr(first(z0, z1))))
   MARK(add(sqr(cons(z0, z1)), x1)) -> c16(A__ADD(a__sqr(cons(mark(z0), z1)), mark(x1)), MARK(sqr(cons(z0, z1))))
   MARK(add(sqr(recip(z0)), x1)) -> c16(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(sqr(recip(z0))))
   MARK(add(sqr(s(z0)), x1)) -> c16(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(sqr(s(z0))))
   MARK(add(sqr(0), x1)) -> c16(A__ADD(a__sqr(0), mark(x1)), MARK(sqr(0)))
   MARK(add(sqr(nil), x1)) -> c16(A__ADD(a__sqr(nil), mark(x1)), MARK(sqr(nil)))
   MARK(add(sqr(x0), x1)) -> c16(MARK(sqr(x0)))
   MARK(add(add(x0, terms(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(add(x0, terms(z0))))
   MARK(add(add(x0, sqr(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(add(x0, sqr(z0))))
   MARK(add(add(x0, add(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, add(z0, z1))))
   MARK(add(add(x0, dbl(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(add(x0, dbl(z0))))
   MARK(add(add(x0, first(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, first(z0, z1))))
   MARK(add(add(x0, cons(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(add(x0, cons(z0, z1))))
   MARK(add(add(x0, recip(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), recip(mark(z0))), mark(x2)), MARK(add(x0, recip(z0))))
   MARK(add(add(x0, s(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), s(z0)), mark(x2)), MARK(add(x0, s(z0))))
   MARK(add(add(x0, 0), x2)) -> c16(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(add(x0, 0)))
   MARK(add(add(x0, nil), x2)) -> c16(A__ADD(a__add(mark(x0), nil), mark(x2)), MARK(add(x0, nil)))
   MARK(add(add(terms(z0), x1), x2)) -> c16(A__ADD(a__add(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(add(terms(z0), x1)))
   MARK(add(add(sqr(z0), x1), x2)) -> c16(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(add(sqr(z0), x1)))
   MARK(add(add(add(z0, z1), x1), x2)) -> c16(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(add(z0, z1), x1)))
   MARK(add(add(dbl(z0), x1), x2)) -> c16(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(add(dbl(z0), x1)))
   MARK(add(add(first(z0, z1), x1), x2)) -> c16(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(first(z0, z1), x1)))
   MARK(add(add(cons(z0, z1), x1), x2)) -> c16(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(add(cons(z0, z1), x1)))
   MARK(add(add(recip(z0), x1), x2)) -> c16(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(add(recip(z0), x1)))
   MARK(add(add(s(z0), x1), x2)) -> c16(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(add(s(z0), x1)))
   MARK(add(add(0, x1), x2)) -> c16(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(add(0, x1)))
   MARK(add(add(nil, x1), x2)) -> c16(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(add(nil, x1)))
   MARK(add(add(x0, x1), x2)) -> c16(MARK(add(x0, x1)))
   MARK(add(dbl(x0), x1)) -> c16(A__ADD(dbl(mark(x0)), mark(x1)), MARK(dbl(x0)))
   MARK(add(dbl(terms(z0)), x1)) -> c16(A__ADD(a__dbl(a__terms(mark(z0))), mark(x1)), MARK(dbl(terms(z0))))
   MARK(add(dbl(sqr(z0)), x1)) -> c16(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(dbl(sqr(z0))))
   MARK(add(dbl(add(z0, z1)), x1)) -> c16(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(dbl(add(z0, z1))))
   MARK(add(dbl(dbl(z0)), x1)) -> c16(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(dbl(dbl(z0))))
   MARK(add(dbl(first(z0, z1)), x1)) -> c16(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(dbl(first(z0, z1))))
   MARK(add(dbl(cons(z0, z1)), x1)) -> c16(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(dbl(cons(z0, z1))))
   MARK(add(dbl(recip(z0)), x1)) -> c16(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(dbl(recip(z0))))
   MARK(add(dbl(s(z0)), x1)) -> c16(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(dbl(s(z0))))
   MARK(add(dbl(0), x1)) -> c16(A__ADD(a__dbl(0), mark(x1)), MARK(dbl(0)))
   MARK(add(dbl(nil), x1)) -> c16(A__ADD(a__dbl(nil), mark(x1)), MARK(dbl(nil)))
   MARK(add(dbl(x0), x1)) -> c16(MARK(dbl(x0)))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1


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

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

(126)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
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   MARK(add(sqr(first(z0, z1)), x1)) -> c16(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), mark(x1)), MARK(sqr(first(z0, z1))))
   MARK(add(sqr(cons(z0, z1)), x1)) -> c16(A__ADD(a__sqr(cons(mark(z0), z1)), mark(x1)), MARK(sqr(cons(z0, z1))))
   MARK(add(sqr(recip(z0)), x1)) -> c16(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(sqr(recip(z0))))
   MARK(add(sqr(s(z0)), x1)) -> c16(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(sqr(s(z0))))
   MARK(add(sqr(0), x1)) -> c16(A__ADD(a__sqr(0), mark(x1)), MARK(sqr(0)))
   MARK(add(sqr(nil), x1)) -> c16(A__ADD(a__sqr(nil), mark(x1)), MARK(sqr(nil)))
   MARK(add(sqr(x0), x1)) -> c16(MARK(sqr(x0)))
   MARK(add(add(x0, terms(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(add(x0, terms(z0))))
   MARK(add(add(x0, sqr(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(add(x0, sqr(z0))))
   MARK(add(add(x0, add(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, add(z0, z1))))
   MARK(add(add(x0, dbl(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(add(x0, dbl(z0))))
   MARK(add(add(x0, first(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, first(z0, z1))))
   MARK(add(add(x0, cons(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(add(x0, cons(z0, z1))))
   MARK(add(add(x0, recip(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), recip(mark(z0))), mark(x2)), MARK(add(x0, recip(z0))))
   MARK(add(add(x0, s(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), s(z0)), mark(x2)), MARK(add(x0, s(z0))))
   MARK(add(add(x0, 0), x2)) -> c16(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(add(x0, 0)))
   MARK(add(add(x0, nil), x2)) -> c16(A__ADD(a__add(mark(x0), nil), mark(x2)), MARK(add(x0, nil)))
   MARK(add(add(terms(z0), x1), x2)) -> c16(A__ADD(a__add(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(add(terms(z0), x1)))
   MARK(add(add(sqr(z0), x1), x2)) -> c16(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(add(sqr(z0), x1)))
   MARK(add(add(add(z0, z1), x1), x2)) -> c16(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(add(z0, z1), x1)))
   MARK(add(add(dbl(z0), x1), x2)) -> c16(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(add(dbl(z0), x1)))
   MARK(add(add(first(z0, z1), x1), x2)) -> c16(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(first(z0, z1), x1)))
   MARK(add(add(cons(z0, z1), x1), x2)) -> c16(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(add(cons(z0, z1), x1)))
   MARK(add(add(recip(z0), x1), x2)) -> c16(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(add(recip(z0), x1)))
   MARK(add(add(s(z0), x1), x2)) -> c16(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(add(s(z0), x1)))
   MARK(add(add(0, x1), x2)) -> c16(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(add(0, x1)))
   MARK(add(add(nil, x1), x2)) -> c16(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(add(nil, x1)))
   MARK(add(add(x0, x1), x2)) -> c16(MARK(add(x0, x1)))
   MARK(add(dbl(terms(z0)), x1)) -> c16(A__ADD(a__dbl(a__terms(mark(z0))), mark(x1)), MARK(dbl(terms(z0))))
   MARK(add(dbl(sqr(z0)), x1)) -> c16(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(dbl(sqr(z0))))
   MARK(add(dbl(add(z0, z1)), x1)) -> c16(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(dbl(add(z0, z1))))
   MARK(add(dbl(dbl(z0)), x1)) -> c16(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(dbl(dbl(z0))))
   MARK(add(dbl(first(z0, z1)), x1)) -> c16(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(dbl(first(z0, z1))))
   MARK(add(dbl(cons(z0, z1)), x1)) -> c16(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(dbl(cons(z0, z1))))
   MARK(add(dbl(recip(z0)), x1)) -> c16(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(dbl(recip(z0))))
   MARK(add(dbl(s(z0)), x1)) -> c16(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(dbl(s(z0))))
   MARK(add(dbl(0), x1)) -> c16(A__ADD(a__dbl(0), mark(x1)), MARK(dbl(0)))
   MARK(add(dbl(nil), x1)) -> c16(A__ADD(a__dbl(nil), mark(x1)), MARK(dbl(nil)))
   MARK(add(dbl(x0), x1)) -> c16(MARK(dbl(x0)))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
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   MARK(add(dbl(sqr(z0)), x1)) -> c16(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(dbl(sqr(z0))))
   MARK(add(dbl(add(z0, z1)), x1)) -> c16(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(dbl(add(z0, z1))))
   MARK(add(dbl(dbl(z0)), x1)) -> c16(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(dbl(dbl(z0))))
   MARK(add(dbl(first(z0, z1)), x1)) -> c16(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(dbl(first(z0, z1))))
   MARK(add(dbl(cons(z0, z1)), x1)) -> c16(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(dbl(cons(z0, z1))))
   MARK(add(dbl(recip(z0)), x1)) -> c16(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(dbl(recip(z0))))
   MARK(add(dbl(s(z0)), x1)) -> c16(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(dbl(s(z0))))
   MARK(add(dbl(0), x1)) -> c16(A__ADD(a__dbl(0), mark(x1)), MARK(dbl(0)))
   MARK(add(dbl(nil), x1)) -> c16(A__ADD(a__dbl(nil), mark(x1)), MARK(dbl(nil)))
   MARK(add(dbl(x0), x1)) -> c16(MARK(dbl(x0)))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1


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

(127) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) by 
   MARK(add(first(x0, x1), terms(z0))) -> c16(A__ADD(a__first(mark(x0), mark(x1)), a__terms(mark(z0))), MARK(first(x0, x1)))
   MARK(add(first(x0, x1), sqr(z0))) -> c16(A__ADD(a__first(mark(x0), mark(x1)), a__sqr(mark(z0))), MARK(first(x0, x1)))
   MARK(add(first(x0, x1), add(z0, z1))) -> c16(A__ADD(a__first(mark(x0), mark(x1)), a__add(mark(z0), mark(z1))), MARK(first(x0, x1)))
   MARK(add(first(x0, x1), dbl(z0))) -> c16(A__ADD(a__first(mark(x0), mark(x1)), a__dbl(mark(z0))), MARK(first(x0, x1)))
   MARK(add(first(x0, x1), first(z0, z1))) -> c16(A__ADD(a__first(mark(x0), mark(x1)), a__first(mark(z0), mark(z1))), MARK(first(x0, x1)))
   MARK(add(first(x0, x1), cons(z0, z1))) -> c16(A__ADD(a__first(mark(x0), mark(x1)), cons(mark(z0), z1)), MARK(first(x0, x1)))
   MARK(add(first(x0, x1), recip(z0))) -> c16(A__ADD(a__first(mark(x0), mark(x1)), recip(mark(z0))), MARK(first(x0, x1)))
   MARK(add(first(x0, x1), s(z0))) -> c16(A__ADD(a__first(mark(x0), mark(x1)), s(z0)), MARK(first(x0, x1)))
   MARK(add(first(x0, x1), 0)) -> c16(A__ADD(a__first(mark(x0), mark(x1)), 0), MARK(first(x0, x1)))
   MARK(add(first(x0, x1), nil)) -> c16(A__ADD(a__first(mark(x0), mark(x1)), nil), MARK(first(x0, x1)))
   MARK(add(first(x0, x1), x2)) -> c16(A__ADD(first(mark(x0), mark(x1)), mark(x2)), MARK(first(x0, x1)))
   MARK(add(first(x0, terms(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(first(x0, terms(z0))))
   MARK(add(first(x0, sqr(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(first(x0, sqr(z0))))
   MARK(add(first(x0, add(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, add(z0, z1))))
   MARK(add(first(x0, dbl(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(first(x0, dbl(z0))))
   MARK(add(first(x0, first(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1))))
   MARK(add(first(x0, cons(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1))))
   MARK(add(first(x0, recip(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), recip(mark(z0))), mark(x2)), MARK(first(x0, recip(z0))))
   MARK(add(first(x0, s(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(first(x0, s(z0))))
   MARK(add(first(x0, 0), x2)) -> c16(A__ADD(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0)))
   MARK(add(first(x0, nil), x2)) -> c16(A__ADD(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil)))
   MARK(add(first(terms(z0), x1), x2)) -> c16(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(first(terms(z0), x1)))
   MARK(add(first(sqr(z0), x1), x2)) -> c16(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(first(sqr(z0), x1)))
   MARK(add(first(add(z0, z1), x1), x2)) -> c16(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(add(z0, z1), x1)))
   MARK(add(first(dbl(z0), x1), x2)) -> c16(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(first(dbl(z0), x1)))
   MARK(add(first(first(z0, z1), x1), x2)) -> c16(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1)))
   MARK(add(first(cons(z0, z1), x1), x2)) -> c16(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1)))
   MARK(add(first(recip(z0), x1), x2)) -> c16(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(first(recip(z0), x1)))
   MARK(add(first(s(z0), x1), x2)) -> c16(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(first(s(z0), x1)))
   MARK(add(first(0, x1), x2)) -> c16(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1)))
   MARK(add(first(nil, x1), x2)) -> c16(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1)))

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

(128)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
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   MARK(add(add(x0, s(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), s(z0)), mark(x2)), MARK(add(x0, s(z0))))
   MARK(add(add(x0, 0), x2)) -> c16(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(add(x0, 0)))
   MARK(add(add(x0, nil), x2)) -> c16(A__ADD(a__add(mark(x0), nil), mark(x2)), MARK(add(x0, nil)))
   MARK(add(add(terms(z0), x1), x2)) -> c16(A__ADD(a__add(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(add(terms(z0), x1)))
   MARK(add(add(sqr(z0), x1), x2)) -> c16(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(add(sqr(z0), x1)))
   MARK(add(add(add(z0, z1), x1), x2)) -> c16(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(add(z0, z1), x1)))
   MARK(add(add(dbl(z0), x1), x2)) -> c16(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(add(dbl(z0), x1)))
   MARK(add(add(first(z0, z1), x1), x2)) -> c16(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(first(z0, z1), x1)))
   MARK(add(add(cons(z0, z1), x1), x2)) -> c16(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(add(cons(z0, z1), x1)))
   MARK(add(add(recip(z0), x1), x2)) -> c16(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(add(recip(z0), x1)))
   MARK(add(add(s(z0), x1), x2)) -> c16(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(add(s(z0), x1)))
   MARK(add(add(0, x1), x2)) -> c16(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(add(0, x1)))
   MARK(add(add(nil, x1), x2)) -> c16(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(add(nil, x1)))
   MARK(add(add(x0, x1), x2)) -> c16(MARK(add(x0, x1)))
   MARK(add(dbl(terms(z0)), x1)) -> c16(A__ADD(a__dbl(a__terms(mark(z0))), mark(x1)), MARK(dbl(terms(z0))))
   MARK(add(dbl(sqr(z0)), x1)) -> c16(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(dbl(sqr(z0))))
   MARK(add(dbl(add(z0, z1)), x1)) -> c16(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(dbl(add(z0, z1))))
   MARK(add(dbl(dbl(z0)), x1)) -> c16(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(dbl(dbl(z0))))
   MARK(add(dbl(first(z0, z1)), x1)) -> c16(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(dbl(first(z0, z1))))
   MARK(add(dbl(cons(z0, z1)), x1)) -> c16(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(dbl(cons(z0, z1))))
   MARK(add(dbl(recip(z0)), x1)) -> c16(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(dbl(recip(z0))))
   MARK(add(dbl(s(z0)), x1)) -> c16(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(dbl(s(z0))))
   MARK(add(dbl(0), x1)) -> c16(A__ADD(a__dbl(0), mark(x1)), MARK(dbl(0)))
   MARK(add(dbl(nil), x1)) -> c16(A__ADD(a__dbl(nil), mark(x1)), MARK(dbl(nil)))
   MARK(add(dbl(x0), x1)) -> c16(MARK(dbl(x0)))
   MARK(add(first(x0, x1), x2)) -> c16(A__ADD(first(mark(x0), mark(x1)), mark(x2)), MARK(first(x0, x1)))
   MARK(add(first(x0, terms(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(first(x0, terms(z0))))
   MARK(add(first(x0, sqr(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(first(x0, sqr(z0))))
   MARK(add(first(x0, add(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, add(z0, z1))))
   MARK(add(first(x0, dbl(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(first(x0, dbl(z0))))
   MARK(add(first(x0, first(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1))))
   MARK(add(first(x0, cons(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1))))
   MARK(add(first(x0, recip(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), recip(mark(z0))), mark(x2)), MARK(first(x0, recip(z0))))
   MARK(add(first(x0, s(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(first(x0, s(z0))))
   MARK(add(first(x0, 0), x2)) -> c16(A__ADD(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0)))
   MARK(add(first(x0, nil), x2)) -> c16(A__ADD(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil)))
   MARK(add(first(terms(z0), x1), x2)) -> c16(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(first(terms(z0), x1)))
   MARK(add(first(sqr(z0), x1), x2)) -> c16(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(first(sqr(z0), x1)))
   MARK(add(first(add(z0, z1), x1), x2)) -> c16(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(add(z0, z1), x1)))
   MARK(add(first(dbl(z0), x1), x2)) -> c16(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(first(dbl(z0), x1)))
   MARK(add(first(first(z0, z1), x1), x2)) -> c16(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1)))
   MARK(add(first(cons(z0, z1), x1), x2)) -> c16(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1)))
   MARK(add(first(recip(z0), x1), x2)) -> c16(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(first(recip(z0), x1)))
   MARK(add(first(s(z0), x1), x2)) -> c16(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(first(s(z0), x1)))
   MARK(add(first(0, x1), x2)) -> c16(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1)))
   MARK(add(first(nil, x1), x2)) -> c16(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1)))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
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   MARK(add(add(first(z0, z1), x1), x2)) -> c16(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(first(z0, z1), x1)))
   MARK(add(add(cons(z0, z1), x1), x2)) -> c16(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(add(cons(z0, z1), x1)))
   MARK(add(add(recip(z0), x1), x2)) -> c16(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(add(recip(z0), x1)))
   MARK(add(add(s(z0), x1), x2)) -> c16(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(add(s(z0), x1)))
   MARK(add(add(0, x1), x2)) -> c16(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(add(0, x1)))
   MARK(add(add(nil, x1), x2)) -> c16(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(add(nil, x1)))
   MARK(add(add(x0, x1), x2)) -> c16(MARK(add(x0, x1)))
   MARK(add(dbl(terms(z0)), x1)) -> c16(A__ADD(a__dbl(a__terms(mark(z0))), mark(x1)), MARK(dbl(terms(z0))))
   MARK(add(dbl(sqr(z0)), x1)) -> c16(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(dbl(sqr(z0))))
   MARK(add(dbl(add(z0, z1)), x1)) -> c16(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(dbl(add(z0, z1))))
   MARK(add(dbl(dbl(z0)), x1)) -> c16(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(dbl(dbl(z0))))
   MARK(add(dbl(first(z0, z1)), x1)) -> c16(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(dbl(first(z0, z1))))
   MARK(add(dbl(cons(z0, z1)), x1)) -> c16(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(dbl(cons(z0, z1))))
   MARK(add(dbl(recip(z0)), x1)) -> c16(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(dbl(recip(z0))))
   MARK(add(dbl(s(z0)), x1)) -> c16(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(dbl(s(z0))))
   MARK(add(dbl(0), x1)) -> c16(A__ADD(a__dbl(0), mark(x1)), MARK(dbl(0)))
   MARK(add(dbl(nil), x1)) -> c16(A__ADD(a__dbl(nil), mark(x1)), MARK(dbl(nil)))
   MARK(add(dbl(x0), x1)) -> c16(MARK(dbl(x0)))
   MARK(add(first(x0, x1), x2)) -> c16(A__ADD(first(mark(x0), mark(x1)), mark(x2)), MARK(first(x0, x1)))
   MARK(add(first(x0, terms(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(first(x0, terms(z0))))
   MARK(add(first(x0, sqr(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(first(x0, sqr(z0))))
   MARK(add(first(x0, add(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, add(z0, z1))))
   MARK(add(first(x0, dbl(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(first(x0, dbl(z0))))
   MARK(add(first(x0, first(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1))))
   MARK(add(first(x0, cons(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1))))
   MARK(add(first(x0, recip(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), recip(mark(z0))), mark(x2)), MARK(first(x0, recip(z0))))
   MARK(add(first(x0, s(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(first(x0, s(z0))))
   MARK(add(first(x0, 0), x2)) -> c16(A__ADD(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0)))
   MARK(add(first(x0, nil), x2)) -> c16(A__ADD(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil)))
   MARK(add(first(terms(z0), x1), x2)) -> c16(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(first(terms(z0), x1)))
   MARK(add(first(sqr(z0), x1), x2)) -> c16(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(first(sqr(z0), x1)))
   MARK(add(first(add(z0, z1), x1), x2)) -> c16(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(add(z0, z1), x1)))
   MARK(add(first(dbl(z0), x1), x2)) -> c16(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(first(dbl(z0), x1)))
   MARK(add(first(first(z0, z1), x1), x2)) -> c16(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1)))
   MARK(add(first(cons(z0, z1), x1), x2)) -> c16(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1)))
   MARK(add(first(recip(z0), x1), x2)) -> c16(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(first(recip(z0), x1)))
   MARK(add(first(s(z0), x1), x2)) -> c16(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(first(s(z0), x1)))
   MARK(add(first(0, x1), x2)) -> c16(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1)))
   MARK(add(first(nil, x1), x2)) -> c16(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1)))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2


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

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

(130)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
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   MARK(add(add(terms(z0), x1), x2)) -> c16(A__ADD(a__add(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(add(terms(z0), x1)))
   MARK(add(add(sqr(z0), x1), x2)) -> c16(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(add(sqr(z0), x1)))
   MARK(add(add(add(z0, z1), x1), x2)) -> c16(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(add(z0, z1), x1)))
   MARK(add(add(dbl(z0), x1), x2)) -> c16(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(add(dbl(z0), x1)))
   MARK(add(add(first(z0, z1), x1), x2)) -> c16(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(first(z0, z1), x1)))
   MARK(add(add(cons(z0, z1), x1), x2)) -> c16(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(add(cons(z0, z1), x1)))
   MARK(add(add(recip(z0), x1), x2)) -> c16(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(add(recip(z0), x1)))
   MARK(add(add(s(z0), x1), x2)) -> c16(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(add(s(z0), x1)))
   MARK(add(add(0, x1), x2)) -> c16(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(add(0, x1)))
   MARK(add(add(nil, x1), x2)) -> c16(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(add(nil, x1)))
   MARK(add(add(x0, x1), x2)) -> c16(MARK(add(x0, x1)))
   MARK(add(dbl(terms(z0)), x1)) -> c16(A__ADD(a__dbl(a__terms(mark(z0))), mark(x1)), MARK(dbl(terms(z0))))
   MARK(add(dbl(sqr(z0)), x1)) -> c16(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(dbl(sqr(z0))))
   MARK(add(dbl(add(z0, z1)), x1)) -> c16(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(dbl(add(z0, z1))))
   MARK(add(dbl(dbl(z0)), x1)) -> c16(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(dbl(dbl(z0))))
   MARK(add(dbl(first(z0, z1)), x1)) -> c16(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(dbl(first(z0, z1))))
   MARK(add(dbl(cons(z0, z1)), x1)) -> c16(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(dbl(cons(z0, z1))))
   MARK(add(dbl(recip(z0)), x1)) -> c16(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(dbl(recip(z0))))
   MARK(add(dbl(s(z0)), x1)) -> c16(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(dbl(s(z0))))
   MARK(add(dbl(0), x1)) -> c16(A__ADD(a__dbl(0), mark(x1)), MARK(dbl(0)))
   MARK(add(dbl(nil), x1)) -> c16(A__ADD(a__dbl(nil), mark(x1)), MARK(dbl(nil)))
   MARK(add(dbl(x0), x1)) -> c16(MARK(dbl(x0)))
   MARK(add(first(x0, terms(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(first(x0, terms(z0))))
   MARK(add(first(x0, sqr(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(first(x0, sqr(z0))))
   MARK(add(first(x0, add(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, add(z0, z1))))
   MARK(add(first(x0, dbl(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(first(x0, dbl(z0))))
   MARK(add(first(x0, first(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1))))
   MARK(add(first(x0, cons(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1))))
   MARK(add(first(x0, recip(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), recip(mark(z0))), mark(x2)), MARK(first(x0, recip(z0))))
   MARK(add(first(x0, s(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(first(x0, s(z0))))
   MARK(add(first(x0, 0), x2)) -> c16(A__ADD(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0)))
   MARK(add(first(x0, nil), x2)) -> c16(A__ADD(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil)))
   MARK(add(first(terms(z0), x1), x2)) -> c16(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(first(terms(z0), x1)))
   MARK(add(first(sqr(z0), x1), x2)) -> c16(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(first(sqr(z0), x1)))
   MARK(add(first(add(z0, z1), x1), x2)) -> c16(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(add(z0, z1), x1)))
   MARK(add(first(dbl(z0), x1), x2)) -> c16(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(first(dbl(z0), x1)))
   MARK(add(first(first(z0, z1), x1), x2)) -> c16(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1)))
   MARK(add(first(cons(z0, z1), x1), x2)) -> c16(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1)))
   MARK(add(first(recip(z0), x1), x2)) -> c16(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(first(recip(z0), x1)))
   MARK(add(first(s(z0), x1), x2)) -> c16(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(first(s(z0), x1)))
   MARK(add(first(0, x1), x2)) -> c16(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1)))
   MARK(add(first(nil, x1), x2)) -> c16(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1)))
   MARK(add(first(x0, x1), x2)) -> c16(MARK(first(x0, x1)))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
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   MARK(add(add(0, x1), x2)) -> c16(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(add(0, x1)))
   MARK(add(add(nil, x1), x2)) -> c16(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(add(nil, x1)))
   MARK(add(add(x0, x1), x2)) -> c16(MARK(add(x0, x1)))
   MARK(add(dbl(terms(z0)), x1)) -> c16(A__ADD(a__dbl(a__terms(mark(z0))), mark(x1)), MARK(dbl(terms(z0))))
   MARK(add(dbl(sqr(z0)), x1)) -> c16(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(dbl(sqr(z0))))
   MARK(add(dbl(add(z0, z1)), x1)) -> c16(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(dbl(add(z0, z1))))
   MARK(add(dbl(dbl(z0)), x1)) -> c16(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(dbl(dbl(z0))))
   MARK(add(dbl(first(z0, z1)), x1)) -> c16(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(dbl(first(z0, z1))))
   MARK(add(dbl(cons(z0, z1)), x1)) -> c16(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(dbl(cons(z0, z1))))
   MARK(add(dbl(recip(z0)), x1)) -> c16(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(dbl(recip(z0))))
   MARK(add(dbl(s(z0)), x1)) -> c16(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(dbl(s(z0))))
   MARK(add(dbl(0), x1)) -> c16(A__ADD(a__dbl(0), mark(x1)), MARK(dbl(0)))
   MARK(add(dbl(nil), x1)) -> c16(A__ADD(a__dbl(nil), mark(x1)), MARK(dbl(nil)))
   MARK(add(dbl(x0), x1)) -> c16(MARK(dbl(x0)))
   MARK(add(first(x0, terms(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(first(x0, terms(z0))))
   MARK(add(first(x0, sqr(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(first(x0, sqr(z0))))
   MARK(add(first(x0, add(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, add(z0, z1))))
   MARK(add(first(x0, dbl(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(first(x0, dbl(z0))))
   MARK(add(first(x0, first(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1))))
   MARK(add(first(x0, cons(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1))))
   MARK(add(first(x0, recip(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), recip(mark(z0))), mark(x2)), MARK(first(x0, recip(z0))))
   MARK(add(first(x0, s(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(first(x0, s(z0))))
   MARK(add(first(x0, 0), x2)) -> c16(A__ADD(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0)))
   MARK(add(first(x0, nil), x2)) -> c16(A__ADD(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil)))
   MARK(add(first(terms(z0), x1), x2)) -> c16(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(first(terms(z0), x1)))
   MARK(add(first(sqr(z0), x1), x2)) -> c16(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(first(sqr(z0), x1)))
   MARK(add(first(add(z0, z1), x1), x2)) -> c16(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(add(z0, z1), x1)))
   MARK(add(first(dbl(z0), x1), x2)) -> c16(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(first(dbl(z0), x1)))
   MARK(add(first(first(z0, z1), x1), x2)) -> c16(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1)))
   MARK(add(first(cons(z0, z1), x1), x2)) -> c16(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1)))
   MARK(add(first(recip(z0), x1), x2)) -> c16(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(first(recip(z0), x1)))
   MARK(add(first(s(z0), x1), x2)) -> c16(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(first(s(z0), x1)))
   MARK(add(first(0, x1), x2)) -> c16(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1)))
   MARK(add(first(nil, x1), x2)) -> c16(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1)))
   MARK(add(first(x0, x1), x2)) -> c16(MARK(first(x0, x1)))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2


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

(131) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) by 
   MARK(add(x0, terms(x1))) -> c17(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(terms(x1)))
   MARK(add(x0, terms(x1))) -> c17(A__ADD(mark(x0), terms(mark(x1))), MARK(terms(x1)))
   MARK(add(x0, terms(terms(z0)))) -> c17(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0))))
   MARK(add(x0, terms(sqr(z0)))) -> c17(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0))))
   MARK(add(x0, terms(add(z0, z1)))) -> c17(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1))))
   MARK(add(x0, terms(dbl(z0)))) -> c17(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0))))
   MARK(add(x0, terms(first(z0, z1)))) -> c17(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1))))
   MARK(add(x0, terms(cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1))))
   MARK(add(x0, terms(recip(z0)))) -> c17(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(terms(recip(z0))))
   MARK(add(x0, terms(s(z0)))) -> c17(A__ADD(mark(x0), a__terms(s(z0))), MARK(terms(s(z0))))
   MARK(add(x0, terms(0))) -> c17(A__ADD(mark(x0), a__terms(0)), MARK(terms(0)))
   MARK(add(x0, terms(nil))) -> c17(A__ADD(mark(x0), a__terms(nil)), MARK(terms(nil)))
   MARK(add(terms(z0), terms(x1))) -> c17(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(x1)))
   MARK(add(sqr(z0), terms(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(terms(x1)))
   MARK(add(add(z0, z1), terms(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(terms(x1)))
   MARK(add(dbl(z0), terms(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(terms(x1)))
   MARK(add(first(z0, z1), terms(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(terms(x1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c17(A__ADD(cons(mark(z0), z1), a__terms(mark(x1))), MARK(terms(x1)))
   MARK(add(recip(z0), terms(x1))) -> c17(A__ADD(recip(mark(z0)), a__terms(mark(x1))), MARK(terms(x1)))
   MARK(add(s(z0), terms(x1))) -> c17(A__ADD(s(z0), a__terms(mark(x1))), MARK(terms(x1)))
   MARK(add(0, terms(x1))) -> c17(A__ADD(0, a__terms(mark(x1))), MARK(terms(x1)))
   MARK(add(nil, terms(x1))) -> c17(A__ADD(nil, a__terms(mark(x1))), MARK(terms(x1)))
   MARK(add(x0, terms(x1))) -> c17(MARK(terms(x1)))

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

(132)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
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   MARK(add(sqr(recip(z0)), x1)) -> c16(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(sqr(recip(z0))))
   MARK(add(sqr(s(z0)), x1)) -> c16(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(sqr(s(z0))))
   MARK(add(sqr(0), x1)) -> c16(A__ADD(a__sqr(0), mark(x1)), MARK(sqr(0)))
   MARK(add(sqr(nil), x1)) -> c16(A__ADD(a__sqr(nil), mark(x1)), MARK(sqr(nil)))
   MARK(add(sqr(x0), x1)) -> c16(MARK(sqr(x0)))
   MARK(add(add(x0, terms(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(add(x0, terms(z0))))
   MARK(add(add(x0, sqr(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(add(x0, sqr(z0))))
   MARK(add(add(x0, add(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, add(z0, z1))))
   MARK(add(add(x0, dbl(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(add(x0, dbl(z0))))
   MARK(add(add(x0, first(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, first(z0, z1))))
   MARK(add(add(x0, cons(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(add(x0, cons(z0, z1))))
   MARK(add(add(x0, recip(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), recip(mark(z0))), mark(x2)), MARK(add(x0, recip(z0))))
   MARK(add(add(x0, s(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), s(z0)), mark(x2)), MARK(add(x0, s(z0))))
   MARK(add(add(x0, 0), x2)) -> c16(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(add(x0, 0)))
   MARK(add(add(x0, nil), x2)) -> c16(A__ADD(a__add(mark(x0), nil), mark(x2)), MARK(add(x0, nil)))
   MARK(add(add(terms(z0), x1), x2)) -> c16(A__ADD(a__add(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(add(terms(z0), x1)))
   MARK(add(add(sqr(z0), x1), x2)) -> c16(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(add(sqr(z0), x1)))
   MARK(add(add(add(z0, z1), x1), x2)) -> c16(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(add(z0, z1), x1)))
   MARK(add(add(dbl(z0), x1), x2)) -> c16(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(add(dbl(z0), x1)))
   MARK(add(add(first(z0, z1), x1), x2)) -> c16(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(first(z0, z1), x1)))
   MARK(add(add(cons(z0, z1), x1), x2)) -> c16(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(add(cons(z0, z1), x1)))
   MARK(add(add(recip(z0), x1), x2)) -> c16(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(add(recip(z0), x1)))
   MARK(add(add(s(z0), x1), x2)) -> c16(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(add(s(z0), x1)))
   MARK(add(add(0, x1), x2)) -> c16(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(add(0, x1)))
   MARK(add(add(nil, x1), x2)) -> c16(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(add(nil, x1)))
   MARK(add(add(x0, x1), x2)) -> c16(MARK(add(x0, x1)))
   MARK(add(dbl(terms(z0)), x1)) -> c16(A__ADD(a__dbl(a__terms(mark(z0))), mark(x1)), MARK(dbl(terms(z0))))
   MARK(add(dbl(sqr(z0)), x1)) -> c16(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(dbl(sqr(z0))))
   MARK(add(dbl(add(z0, z1)), x1)) -> c16(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(dbl(add(z0, z1))))
   MARK(add(dbl(dbl(z0)), x1)) -> c16(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(dbl(dbl(z0))))
   MARK(add(dbl(first(z0, z1)), x1)) -> c16(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(dbl(first(z0, z1))))
   MARK(add(dbl(cons(z0, z1)), x1)) -> c16(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(dbl(cons(z0, z1))))
   MARK(add(dbl(recip(z0)), x1)) -> c16(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(dbl(recip(z0))))
   MARK(add(dbl(s(z0)), x1)) -> c16(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(dbl(s(z0))))
   MARK(add(dbl(0), x1)) -> c16(A__ADD(a__dbl(0), mark(x1)), MARK(dbl(0)))
   MARK(add(dbl(nil), x1)) -> c16(A__ADD(a__dbl(nil), mark(x1)), MARK(dbl(nil)))
   MARK(add(dbl(x0), x1)) -> c16(MARK(dbl(x0)))
   MARK(add(first(x0, terms(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(first(x0, terms(z0))))
   MARK(add(first(x0, sqr(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(first(x0, sqr(z0))))
   MARK(add(first(x0, add(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, add(z0, z1))))
   MARK(add(first(x0, dbl(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(first(x0, dbl(z0))))
   MARK(add(first(x0, first(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1))))
   MARK(add(first(x0, cons(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1))))
   MARK(add(first(x0, recip(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), recip(mark(z0))), mark(x2)), MARK(first(x0, recip(z0))))
   MARK(add(first(x0, s(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(first(x0, s(z0))))
   MARK(add(first(x0, 0), x2)) -> c16(A__ADD(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0)))
   MARK(add(first(x0, nil), x2)) -> c16(A__ADD(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil)))
   MARK(add(first(terms(z0), x1), x2)) -> c16(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(first(terms(z0), x1)))
   MARK(add(first(sqr(z0), x1), x2)) -> c16(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(first(sqr(z0), x1)))
   MARK(add(first(add(z0, z1), x1), x2)) -> c16(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(add(z0, z1), x1)))
   MARK(add(first(dbl(z0), x1), x2)) -> c16(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(first(dbl(z0), x1)))
   MARK(add(first(first(z0, z1), x1), x2)) -> c16(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1)))
   MARK(add(first(cons(z0, z1), x1), x2)) -> c16(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1)))
   MARK(add(first(recip(z0), x1), x2)) -> c16(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(first(recip(z0), x1)))
   MARK(add(first(s(z0), x1), x2)) -> c16(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(first(s(z0), x1)))
   MARK(add(first(0, x1), x2)) -> c16(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1)))
   MARK(add(first(nil, x1), x2)) -> c16(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1)))
   MARK(add(first(x0, x1), x2)) -> c16(MARK(first(x0, x1)))
   MARK(add(x0, terms(x1))) -> c17(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(terms(x1)))
   MARK(add(x0, terms(x1))) -> c17(A__ADD(mark(x0), terms(mark(x1))), MARK(terms(x1)))
   MARK(add(x0, terms(terms(z0)))) -> c17(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0))))
   MARK(add(x0, terms(sqr(z0)))) -> c17(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0))))
   MARK(add(x0, terms(add(z0, z1)))) -> c17(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1))))
   MARK(add(x0, terms(dbl(z0)))) -> c17(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0))))
   MARK(add(x0, terms(first(z0, z1)))) -> c17(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1))))
   MARK(add(x0, terms(cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1))))
   MARK(add(x0, terms(recip(z0)))) -> c17(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(terms(recip(z0))))
   MARK(add(x0, terms(s(z0)))) -> c17(A__ADD(mark(x0), a__terms(s(z0))), MARK(terms(s(z0))))
   MARK(add(x0, terms(0))) -> c17(A__ADD(mark(x0), a__terms(0)), MARK(terms(0)))
   MARK(add(x0, terms(nil))) -> c17(A__ADD(mark(x0), a__terms(nil)), MARK(terms(nil)))
   MARK(add(terms(z0), terms(x1))) -> c17(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(x1)))
   MARK(add(sqr(z0), terms(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(terms(x1)))
   MARK(add(add(z0, z1), terms(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(terms(x1)))
   MARK(add(dbl(z0), terms(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(terms(x1)))
   MARK(add(first(z0, z1), terms(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(terms(x1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c17(A__ADD(cons(mark(z0), z1), a__terms(mark(x1))), MARK(terms(x1)))
   MARK(add(recip(z0), terms(x1))) -> c17(A__ADD(recip(mark(z0)), a__terms(mark(x1))), MARK(terms(x1)))
   MARK(add(s(z0), terms(x1))) -> c17(A__ADD(s(z0), a__terms(mark(x1))), MARK(terms(x1)))
   MARK(add(0, terms(x1))) -> c17(A__ADD(0, a__terms(mark(x1))), MARK(terms(x1)))
   MARK(add(nil, terms(x1))) -> c17(A__ADD(nil, a__terms(mark(x1))), MARK(terms(x1)))
   MARK(add(x0, terms(x1))) -> c17(MARK(terms(x1)))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
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   MARK(add(terms(recip(z0)), x1)) -> c16(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(terms(recip(z0))))
   MARK(add(terms(s(z0)), x1)) -> c16(A__ADD(a__terms(s(z0)), mark(x1)), MARK(terms(s(z0))))
   MARK(add(terms(0), x1)) -> c16(A__ADD(a__terms(0), mark(x1)), MARK(terms(0)))
   MARK(add(terms(nil), x1)) -> c16(A__ADD(a__terms(nil), mark(x1)), MARK(terms(nil)))
   MARK(add(terms(x0), x1)) -> c16(MARK(terms(x0)))
   MARK(add(sqr(terms(z0)), x1)) -> c16(A__ADD(a__sqr(a__terms(mark(z0))), mark(x1)), MARK(sqr(terms(z0))))
   MARK(add(sqr(sqr(z0)), x1)) -> c16(A__ADD(a__sqr(a__sqr(mark(z0))), mark(x1)), MARK(sqr(sqr(z0))))
   MARK(add(sqr(add(z0, z1)), x1)) -> c16(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), mark(x1)), MARK(sqr(add(z0, z1))))
   MARK(add(sqr(dbl(z0)), x1)) -> c16(A__ADD(a__sqr(a__dbl(mark(z0))), mark(x1)), MARK(sqr(dbl(z0))))
   MARK(add(sqr(first(z0, z1)), x1)) -> c16(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), mark(x1)), MARK(sqr(first(z0, z1))))
   MARK(add(sqr(cons(z0, z1)), x1)) -> c16(A__ADD(a__sqr(cons(mark(z0), z1)), mark(x1)), MARK(sqr(cons(z0, z1))))
   MARK(add(sqr(recip(z0)), x1)) -> c16(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(sqr(recip(z0))))
   MARK(add(sqr(s(z0)), x1)) -> c16(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(sqr(s(z0))))
   MARK(add(sqr(0), x1)) -> c16(A__ADD(a__sqr(0), mark(x1)), MARK(sqr(0)))
   MARK(add(sqr(nil), x1)) -> c16(A__ADD(a__sqr(nil), mark(x1)), MARK(sqr(nil)))
   MARK(add(sqr(x0), x1)) -> c16(MARK(sqr(x0)))
   MARK(add(add(x0, terms(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(add(x0, terms(z0))))
   MARK(add(add(x0, sqr(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(add(x0, sqr(z0))))
   MARK(add(add(x0, add(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, add(z0, z1))))
   MARK(add(add(x0, dbl(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(add(x0, dbl(z0))))
   MARK(add(add(x0, first(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, first(z0, z1))))
   MARK(add(add(x0, cons(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(add(x0, cons(z0, z1))))
   MARK(add(add(x0, recip(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), recip(mark(z0))), mark(x2)), MARK(add(x0, recip(z0))))
   MARK(add(add(x0, s(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), s(z0)), mark(x2)), MARK(add(x0, s(z0))))
   MARK(add(add(x0, 0), x2)) -> c16(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(add(x0, 0)))
   MARK(add(add(x0, nil), x2)) -> c16(A__ADD(a__add(mark(x0), nil), mark(x2)), MARK(add(x0, nil)))
   MARK(add(add(terms(z0), x1), x2)) -> c16(A__ADD(a__add(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(add(terms(z0), x1)))
   MARK(add(add(sqr(z0), x1), x2)) -> c16(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(add(sqr(z0), x1)))
   MARK(add(add(add(z0, z1), x1), x2)) -> c16(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(add(z0, z1), x1)))
   MARK(add(add(dbl(z0), x1), x2)) -> c16(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(add(dbl(z0), x1)))
   MARK(add(add(first(z0, z1), x1), x2)) -> c16(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(first(z0, z1), x1)))
   MARK(add(add(cons(z0, z1), x1), x2)) -> c16(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(add(cons(z0, z1), x1)))
   MARK(add(add(recip(z0), x1), x2)) -> c16(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(add(recip(z0), x1)))
   MARK(add(add(s(z0), x1), x2)) -> c16(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(add(s(z0), x1)))
   MARK(add(add(0, x1), x2)) -> c16(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(add(0, x1)))
   MARK(add(add(nil, x1), x2)) -> c16(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(add(nil, x1)))
   MARK(add(add(x0, x1), x2)) -> c16(MARK(add(x0, x1)))
   MARK(add(dbl(terms(z0)), x1)) -> c16(A__ADD(a__dbl(a__terms(mark(z0))), mark(x1)), MARK(dbl(terms(z0))))
   MARK(add(dbl(sqr(z0)), x1)) -> c16(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(dbl(sqr(z0))))
   MARK(add(dbl(add(z0, z1)), x1)) -> c16(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(dbl(add(z0, z1))))
   MARK(add(dbl(dbl(z0)), x1)) -> c16(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(dbl(dbl(z0))))
   MARK(add(dbl(first(z0, z1)), x1)) -> c16(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(dbl(first(z0, z1))))
   MARK(add(dbl(cons(z0, z1)), x1)) -> c16(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(dbl(cons(z0, z1))))
   MARK(add(dbl(recip(z0)), x1)) -> c16(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(dbl(recip(z0))))
   MARK(add(dbl(s(z0)), x1)) -> c16(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(dbl(s(z0))))
   MARK(add(dbl(0), x1)) -> c16(A__ADD(a__dbl(0), mark(x1)), MARK(dbl(0)))
   MARK(add(dbl(nil), x1)) -> c16(A__ADD(a__dbl(nil), mark(x1)), MARK(dbl(nil)))
   MARK(add(dbl(x0), x1)) -> c16(MARK(dbl(x0)))
   MARK(add(first(x0, terms(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(first(x0, terms(z0))))
   MARK(add(first(x0, sqr(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(first(x0, sqr(z0))))
   MARK(add(first(x0, add(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, add(z0, z1))))
   MARK(add(first(x0, dbl(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(first(x0, dbl(z0))))
   MARK(add(first(x0, first(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1))))
   MARK(add(first(x0, cons(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1))))
   MARK(add(first(x0, recip(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), recip(mark(z0))), mark(x2)), MARK(first(x0, recip(z0))))
   MARK(add(first(x0, s(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(first(x0, s(z0))))
   MARK(add(first(x0, 0), x2)) -> c16(A__ADD(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0)))
   MARK(add(first(x0, nil), x2)) -> c16(A__ADD(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil)))
   MARK(add(first(terms(z0), x1), x2)) -> c16(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(first(terms(z0), x1)))
   MARK(add(first(sqr(z0), x1), x2)) -> c16(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(first(sqr(z0), x1)))
   MARK(add(first(add(z0, z1), x1), x2)) -> c16(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(add(z0, z1), x1)))
   MARK(add(first(dbl(z0), x1), x2)) -> c16(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(first(dbl(z0), x1)))
   MARK(add(first(first(z0, z1), x1), x2)) -> c16(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1)))
   MARK(add(first(cons(z0, z1), x1), x2)) -> c16(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1)))
   MARK(add(first(recip(z0), x1), x2)) -> c16(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(first(recip(z0), x1)))
   MARK(add(first(s(z0), x1), x2)) -> c16(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(first(s(z0), x1)))
   MARK(add(first(0, x1), x2)) -> c16(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1)))
   MARK(add(first(nil, x1), x2)) -> c16(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1)))
   MARK(add(first(x0, x1), x2)) -> c16(MARK(first(x0, x1)))
   MARK(add(x0, terms(x1))) -> c17(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(terms(x1)))
   MARK(add(x0, terms(x1))) -> c17(A__ADD(mark(x0), terms(mark(x1))), MARK(terms(x1)))
   MARK(add(x0, terms(terms(z0)))) -> c17(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0))))
   MARK(add(x0, terms(sqr(z0)))) -> c17(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0))))
   MARK(add(x0, terms(add(z0, z1)))) -> c17(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1))))
   MARK(add(x0, terms(dbl(z0)))) -> c17(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0))))
   MARK(add(x0, terms(first(z0, z1)))) -> c17(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1))))
   MARK(add(x0, terms(cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1))))
   MARK(add(x0, terms(recip(z0)))) -> c17(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(terms(recip(z0))))
   MARK(add(x0, terms(s(z0)))) -> c17(A__ADD(mark(x0), a__terms(s(z0))), MARK(terms(s(z0))))
   MARK(add(x0, terms(0))) -> c17(A__ADD(mark(x0), a__terms(0)), MARK(terms(0)))
   MARK(add(x0, terms(nil))) -> c17(A__ADD(mark(x0), a__terms(nil)), MARK(terms(nil)))
   MARK(add(terms(z0), terms(x1))) -> c17(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(x1)))
   MARK(add(sqr(z0), terms(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(terms(x1)))
   MARK(add(add(z0, z1), terms(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(terms(x1)))
   MARK(add(dbl(z0), terms(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(terms(x1)))
   MARK(add(first(z0, z1), terms(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(terms(x1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c17(A__ADD(cons(mark(z0), z1), a__terms(mark(x1))), MARK(terms(x1)))
   MARK(add(recip(z0), terms(x1))) -> c17(A__ADD(recip(mark(z0)), a__terms(mark(x1))), MARK(terms(x1)))
   MARK(add(s(z0), terms(x1))) -> c17(A__ADD(s(z0), a__terms(mark(x1))), MARK(terms(x1)))
   MARK(add(0, terms(x1))) -> c17(A__ADD(0, a__terms(mark(x1))), MARK(terms(x1)))
   MARK(add(nil, terms(x1))) -> c17(A__ADD(nil, a__terms(mark(x1))), MARK(terms(x1)))
   MARK(add(x0, terms(x1))) -> c17(MARK(terms(x1)))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2


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

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

(134)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
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   MARK(add(sqr(z0), s(x1))) -> c16(A__ADD(a__sqr(mark(z0)), s(x1)), MARK(sqr(z0)))
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   MARK(add(recip(z0), s(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, s(x1))) -> c16(A__ADD(0, s(x1)))
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   MARK(add(cons(z0, z1), 0)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), 0)) -> c16(MARK(recip(z0)))
   MARK(add(0, 0)) -> c16(A__ADD(0, 0))
   MARK(add(terms(z0), nil)) -> c16(A__ADD(a__terms(mark(z0)), nil), MARK(terms(z0)))
   MARK(add(sqr(z0), nil)) -> c16(A__ADD(a__sqr(mark(z0)), nil), MARK(sqr(z0)))
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   MARK(add(dbl(z0), nil)) -> c16(A__ADD(a__dbl(mark(z0)), nil), MARK(dbl(z0)))
   MARK(add(first(z0, z1), nil)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), nil), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), nil)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), nil)) -> c16(MARK(recip(z0)))
   MARK(add(0, nil)) -> c16(A__ADD(0, nil))
   MARK(add(terms(terms(z0)), x1)) -> c16(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(terms(terms(z0))))
   MARK(add(terms(sqr(z0)), x1)) -> c16(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(terms(sqr(z0))))
   MARK(add(terms(add(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(terms(add(z0, z1))))
   MARK(add(terms(dbl(z0)), x1)) -> c16(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(terms(dbl(z0))))
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   MARK(add(terms(recip(z0)), x1)) -> c16(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(terms(recip(z0))))
   MARK(add(terms(s(z0)), x1)) -> c16(A__ADD(a__terms(s(z0)), mark(x1)), MARK(terms(s(z0))))
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   MARK(add(terms(nil), x1)) -> c16(A__ADD(a__terms(nil), mark(x1)), MARK(terms(nil)))
   MARK(add(terms(x0), x1)) -> c16(MARK(terms(x0)))
   MARK(add(sqr(terms(z0)), x1)) -> c16(A__ADD(a__sqr(a__terms(mark(z0))), mark(x1)), MARK(sqr(terms(z0))))
   MARK(add(sqr(sqr(z0)), x1)) -> c16(A__ADD(a__sqr(a__sqr(mark(z0))), mark(x1)), MARK(sqr(sqr(z0))))
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   MARK(add(sqr(dbl(z0)), x1)) -> c16(A__ADD(a__sqr(a__dbl(mark(z0))), mark(x1)), MARK(sqr(dbl(z0))))
   MARK(add(sqr(first(z0, z1)), x1)) -> c16(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), mark(x1)), MARK(sqr(first(z0, z1))))
   MARK(add(sqr(cons(z0, z1)), x1)) -> c16(A__ADD(a__sqr(cons(mark(z0), z1)), mark(x1)), MARK(sqr(cons(z0, z1))))
   MARK(add(sqr(recip(z0)), x1)) -> c16(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(sqr(recip(z0))))
   MARK(add(sqr(s(z0)), x1)) -> c16(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(sqr(s(z0))))
   MARK(add(sqr(0), x1)) -> c16(A__ADD(a__sqr(0), mark(x1)), MARK(sqr(0)))
   MARK(add(sqr(nil), x1)) -> c16(A__ADD(a__sqr(nil), mark(x1)), MARK(sqr(nil)))
   MARK(add(sqr(x0), x1)) -> c16(MARK(sqr(x0)))
   MARK(add(add(x0, terms(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(add(x0, terms(z0))))
   MARK(add(add(x0, sqr(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(add(x0, sqr(z0))))
   MARK(add(add(x0, add(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, add(z0, z1))))
   MARK(add(add(x0, dbl(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(add(x0, dbl(z0))))
   MARK(add(add(x0, first(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, first(z0, z1))))
   MARK(add(add(x0, cons(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(add(x0, cons(z0, z1))))
   MARK(add(add(x0, recip(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), recip(mark(z0))), mark(x2)), MARK(add(x0, recip(z0))))
   MARK(add(add(x0, s(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), s(z0)), mark(x2)), MARK(add(x0, s(z0))))
   MARK(add(add(x0, 0), x2)) -> c16(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(add(x0, 0)))
   MARK(add(add(x0, nil), x2)) -> c16(A__ADD(a__add(mark(x0), nil), mark(x2)), MARK(add(x0, nil)))
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   MARK(add(add(sqr(z0), x1), x2)) -> c16(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(add(sqr(z0), x1)))
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   MARK(add(add(recip(z0), x1), x2)) -> c16(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(add(recip(z0), x1)))
   MARK(add(add(s(z0), x1), x2)) -> c16(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(add(s(z0), x1)))
   MARK(add(add(0, x1), x2)) -> c16(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(add(0, x1)))
   MARK(add(add(nil, x1), x2)) -> c16(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(add(nil, x1)))
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   MARK(add(dbl(sqr(z0)), x1)) -> c16(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(dbl(sqr(z0))))
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   MARK(add(dbl(recip(z0)), x1)) -> c16(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(dbl(recip(z0))))
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   MARK(add(first(x0, sqr(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(first(x0, sqr(z0))))
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   MARK(add(first(x0, first(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1))))
   MARK(add(first(x0, cons(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1))))
   MARK(add(first(x0, recip(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), recip(mark(z0))), mark(x2)), MARK(first(x0, recip(z0))))
   MARK(add(first(x0, s(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(first(x0, s(z0))))
   MARK(add(first(x0, 0), x2)) -> c16(A__ADD(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0)))
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   MARK(add(first(sqr(z0), x1), x2)) -> c16(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(first(sqr(z0), x1)))
   MARK(add(first(add(z0, z1), x1), x2)) -> c16(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(add(z0, z1), x1)))
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   MARK(add(cons(z0, z1), terms(x1))) -> c17(MARK(terms(x1)))
   MARK(add(recip(z0), terms(x1))) -> c17(MARK(terms(x1)))
   MARK(add(s(z0), terms(x1))) -> c17(MARK(terms(x1)))
   MARK(add(nil, terms(x1))) -> c17(MARK(terms(x1)))
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   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
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   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
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   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
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   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
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   MARK(add(x0, recip(nil))) -> c16(A__ADD(mark(x0), recip(nil)), MARK(x0))
   MARK(add(terms(z0), recip(x1))) -> c16(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), recip(x1))) -> c16(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), recip(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), recip(x1))) -> c16(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), recip(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), recip(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), recip(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, recip(x1))) -> c16(A__ADD(0, recip(mark(x1))))
   MARK(add(terms(z0), s(x1))) -> c16(A__ADD(a__terms(mark(z0)), s(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), s(x1))) -> c16(A__ADD(a__sqr(mark(z0)), s(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), s(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), s(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), s(x1))) -> c16(A__ADD(a__dbl(mark(z0)), s(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), s(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), s(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), s(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), s(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, s(x1))) -> c16(A__ADD(0, s(x1)))
   MARK(add(terms(z0), 0)) -> c16(A__ADD(a__terms(mark(z0)), 0), MARK(terms(z0)))
   MARK(add(sqr(z0), 0)) -> c16(A__ADD(a__sqr(mark(z0)), 0), MARK(sqr(z0)))
   MARK(add(add(z0, z1), 0)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1)))
   MARK(add(dbl(z0), 0)) -> c16(A__ADD(a__dbl(mark(z0)), 0), MARK(dbl(z0)))
   MARK(add(first(z0, z1), 0)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), 0), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), 0)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), 0)) -> c16(MARK(recip(z0)))
   MARK(add(0, 0)) -> c16(A__ADD(0, 0))
   MARK(add(terms(z0), nil)) -> c16(A__ADD(a__terms(mark(z0)), nil), MARK(terms(z0)))
   MARK(add(sqr(z0), nil)) -> c16(A__ADD(a__sqr(mark(z0)), nil), MARK(sqr(z0)))
   MARK(add(add(z0, z1), nil)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), nil), MARK(add(z0, z1)))
   MARK(add(dbl(z0), nil)) -> c16(A__ADD(a__dbl(mark(z0)), nil), MARK(dbl(z0)))
   MARK(add(first(z0, z1), nil)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), nil), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), nil)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), nil)) -> c16(MARK(recip(z0)))
   MARK(add(0, nil)) -> c16(A__ADD(0, nil))
   MARK(add(terms(terms(z0)), x1)) -> c16(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(terms(terms(z0))))
   MARK(add(terms(sqr(z0)), x1)) -> c16(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(terms(sqr(z0))))
   MARK(add(terms(add(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(terms(add(z0, z1))))
   MARK(add(terms(dbl(z0)), x1)) -> c16(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(terms(dbl(z0))))
   MARK(add(terms(first(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(terms(first(z0, z1))))
   MARK(add(terms(cons(z0, z1)), x1)) -> c16(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(terms(cons(z0, z1))))
   MARK(add(terms(recip(z0)), x1)) -> c16(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(terms(recip(z0))))
   MARK(add(terms(s(z0)), x1)) -> c16(A__ADD(a__terms(s(z0)), mark(x1)), MARK(terms(s(z0))))
   MARK(add(terms(0), x1)) -> c16(A__ADD(a__terms(0), mark(x1)), MARK(terms(0)))
   MARK(add(terms(nil), x1)) -> c16(A__ADD(a__terms(nil), mark(x1)), MARK(terms(nil)))
   MARK(add(terms(x0), x1)) -> c16(MARK(terms(x0)))
   MARK(add(sqr(terms(z0)), x1)) -> c16(A__ADD(a__sqr(a__terms(mark(z0))), mark(x1)), MARK(sqr(terms(z0))))
   MARK(add(sqr(sqr(z0)), x1)) -> c16(A__ADD(a__sqr(a__sqr(mark(z0))), mark(x1)), MARK(sqr(sqr(z0))))
   MARK(add(sqr(add(z0, z1)), x1)) -> c16(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), mark(x1)), MARK(sqr(add(z0, z1))))
   MARK(add(sqr(dbl(z0)), x1)) -> c16(A__ADD(a__sqr(a__dbl(mark(z0))), mark(x1)), MARK(sqr(dbl(z0))))
   MARK(add(sqr(first(z0, z1)), x1)) -> c16(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), mark(x1)), MARK(sqr(first(z0, z1))))
   MARK(add(sqr(cons(z0, z1)), x1)) -> c16(A__ADD(a__sqr(cons(mark(z0), z1)), mark(x1)), MARK(sqr(cons(z0, z1))))
   MARK(add(sqr(recip(z0)), x1)) -> c16(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(sqr(recip(z0))))
   MARK(add(sqr(s(z0)), x1)) -> c16(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(sqr(s(z0))))
   MARK(add(sqr(0), x1)) -> c16(A__ADD(a__sqr(0), mark(x1)), MARK(sqr(0)))
   MARK(add(sqr(nil), x1)) -> c16(A__ADD(a__sqr(nil), mark(x1)), MARK(sqr(nil)))
   MARK(add(sqr(x0), x1)) -> c16(MARK(sqr(x0)))
   MARK(add(add(x0, terms(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(add(x0, terms(z0))))
   MARK(add(add(x0, sqr(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(add(x0, sqr(z0))))
   MARK(add(add(x0, add(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, add(z0, z1))))
   MARK(add(add(x0, dbl(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(add(x0, dbl(z0))))
   MARK(add(add(x0, first(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, first(z0, z1))))
   MARK(add(add(x0, cons(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(add(x0, cons(z0, z1))))
   MARK(add(add(x0, recip(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), recip(mark(z0))), mark(x2)), MARK(add(x0, recip(z0))))
   MARK(add(add(x0, s(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), s(z0)), mark(x2)), MARK(add(x0, s(z0))))
   MARK(add(add(x0, 0), x2)) -> c16(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(add(x0, 0)))
   MARK(add(add(x0, nil), x2)) -> c16(A__ADD(a__add(mark(x0), nil), mark(x2)), MARK(add(x0, nil)))
   MARK(add(add(terms(z0), x1), x2)) -> c16(A__ADD(a__add(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(add(terms(z0), x1)))
   MARK(add(add(sqr(z0), x1), x2)) -> c16(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(add(sqr(z0), x1)))
   MARK(add(add(add(z0, z1), x1), x2)) -> c16(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(add(z0, z1), x1)))
   MARK(add(add(dbl(z0), x1), x2)) -> c16(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(add(dbl(z0), x1)))
   MARK(add(add(first(z0, z1), x1), x2)) -> c16(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(first(z0, z1), x1)))
   MARK(add(add(cons(z0, z1), x1), x2)) -> c16(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(add(cons(z0, z1), x1)))
   MARK(add(add(recip(z0), x1), x2)) -> c16(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(add(recip(z0), x1)))
   MARK(add(add(s(z0), x1), x2)) -> c16(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(add(s(z0), x1)))
   MARK(add(add(0, x1), x2)) -> c16(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(add(0, x1)))
   MARK(add(add(nil, x1), x2)) -> c16(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(add(nil, x1)))
   MARK(add(add(x0, x1), x2)) -> c16(MARK(add(x0, x1)))
   MARK(add(dbl(terms(z0)), x1)) -> c16(A__ADD(a__dbl(a__terms(mark(z0))), mark(x1)), MARK(dbl(terms(z0))))
   MARK(add(dbl(sqr(z0)), x1)) -> c16(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(dbl(sqr(z0))))
   MARK(add(dbl(add(z0, z1)), x1)) -> c16(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(dbl(add(z0, z1))))
   MARK(add(dbl(dbl(z0)), x1)) -> c16(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(dbl(dbl(z0))))
   MARK(add(dbl(first(z0, z1)), x1)) -> c16(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(dbl(first(z0, z1))))
   MARK(add(dbl(cons(z0, z1)), x1)) -> c16(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(dbl(cons(z0, z1))))
   MARK(add(dbl(recip(z0)), x1)) -> c16(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(dbl(recip(z0))))
   MARK(add(dbl(s(z0)), x1)) -> c16(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(dbl(s(z0))))
   MARK(add(dbl(0), x1)) -> c16(A__ADD(a__dbl(0), mark(x1)), MARK(dbl(0)))
   MARK(add(dbl(nil), x1)) -> c16(A__ADD(a__dbl(nil), mark(x1)), MARK(dbl(nil)))
   MARK(add(dbl(x0), x1)) -> c16(MARK(dbl(x0)))
   MARK(add(first(x0, terms(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(first(x0, terms(z0))))
   MARK(add(first(x0, sqr(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(first(x0, sqr(z0))))
   MARK(add(first(x0, add(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, add(z0, z1))))
   MARK(add(first(x0, dbl(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(first(x0, dbl(z0))))
   MARK(add(first(x0, first(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1))))
   MARK(add(first(x0, cons(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1))))
   MARK(add(first(x0, recip(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), recip(mark(z0))), mark(x2)), MARK(first(x0, recip(z0))))
   MARK(add(first(x0, s(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(first(x0, s(z0))))
   MARK(add(first(x0, 0), x2)) -> c16(A__ADD(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0)))
   MARK(add(first(x0, nil), x2)) -> c16(A__ADD(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil)))
   MARK(add(first(terms(z0), x1), x2)) -> c16(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(first(terms(z0), x1)))
   MARK(add(first(sqr(z0), x1), x2)) -> c16(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(first(sqr(z0), x1)))
   MARK(add(first(add(z0, z1), x1), x2)) -> c16(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(add(z0, z1), x1)))
   MARK(add(first(dbl(z0), x1), x2)) -> c16(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(first(dbl(z0), x1)))
   MARK(add(first(first(z0, z1), x1), x2)) -> c16(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1)))
   MARK(add(first(cons(z0, z1), x1), x2)) -> c16(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1)))
   MARK(add(first(recip(z0), x1), x2)) -> c16(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(first(recip(z0), x1)))
   MARK(add(first(s(z0), x1), x2)) -> c16(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(first(s(z0), x1)))
   MARK(add(first(0, x1), x2)) -> c16(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1)))
   MARK(add(first(nil, x1), x2)) -> c16(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1)))
   MARK(add(first(x0, x1), x2)) -> c16(MARK(first(x0, x1)))
   MARK(add(x0, terms(x1))) -> c17(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(terms(x1)))
   MARK(add(x0, terms(x1))) -> c17(A__ADD(mark(x0), terms(mark(x1))), MARK(terms(x1)))
   MARK(add(x0, terms(terms(z0)))) -> c17(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0))))
   MARK(add(x0, terms(sqr(z0)))) -> c17(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0))))
   MARK(add(x0, terms(add(z0, z1)))) -> c17(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1))))
   MARK(add(x0, terms(dbl(z0)))) -> c17(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0))))
   MARK(add(x0, terms(first(z0, z1)))) -> c17(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1))))
   MARK(add(x0, terms(cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1))))
   MARK(add(x0, terms(recip(z0)))) -> c17(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(terms(recip(z0))))
   MARK(add(x0, terms(s(z0)))) -> c17(A__ADD(mark(x0), a__terms(s(z0))), MARK(terms(s(z0))))
   MARK(add(x0, terms(0))) -> c17(A__ADD(mark(x0), a__terms(0)), MARK(terms(0)))
   MARK(add(x0, terms(nil))) -> c17(A__ADD(mark(x0), a__terms(nil)), MARK(terms(nil)))
   MARK(add(terms(z0), terms(x1))) -> c17(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(x1)))
   MARK(add(sqr(z0), terms(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(terms(x1)))
   MARK(add(add(z0, z1), terms(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(terms(x1)))
   MARK(add(dbl(z0), terms(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(terms(x1)))
   MARK(add(first(z0, z1), terms(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(terms(x1)))
   MARK(add(0, terms(x1))) -> c17(A__ADD(0, a__terms(mark(x1))), MARK(terms(x1)))
   MARK(add(x0, terms(x1))) -> c17(MARK(terms(x1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c17(MARK(terms(x1)))
   MARK(add(recip(z0), terms(x1))) -> c17(MARK(terms(x1)))
   MARK(add(s(z0), terms(x1))) -> c17(MARK(terms(x1)))
   MARK(add(nil, terms(x1))) -> c17(MARK(terms(x1)))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2


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

(135) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) by 
   MARK(add(x0, sqr(x1))) -> c17(A__ADD(mark(x0), sqr(mark(x1))), MARK(sqr(x1)))
   MARK(add(x0, sqr(terms(z0)))) -> c17(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0))))
   MARK(add(x0, sqr(sqr(z0)))) -> c17(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0))))
   MARK(add(x0, sqr(add(z0, z1)))) -> c17(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1))))
   MARK(add(x0, sqr(dbl(z0)))) -> c17(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0))))
   MARK(add(x0, sqr(first(z0, z1)))) -> c17(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1))))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1))))
   MARK(add(x0, sqr(recip(z0)))) -> c17(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0))))
   MARK(add(x0, sqr(s(z0)))) -> c17(A__ADD(mark(x0), a__sqr(s(z0))), MARK(sqr(s(z0))))
   MARK(add(x0, sqr(0))) -> c17(A__ADD(mark(x0), a__sqr(0)), MARK(sqr(0)))
   MARK(add(x0, sqr(nil))) -> c17(A__ADD(mark(x0), a__sqr(nil)), MARK(sqr(nil)))
   MARK(add(terms(z0), sqr(x1))) -> c17(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(sqr(x1)))
   MARK(add(sqr(z0), sqr(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(x1)))
   MARK(add(add(z0, z1), sqr(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(sqr(x1)))
   MARK(add(dbl(z0), sqr(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(sqr(x1)))
   MARK(add(first(z0, z1), sqr(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(sqr(x1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c17(A__ADD(cons(mark(z0), z1), a__sqr(mark(x1))), MARK(sqr(x1)))
   MARK(add(recip(z0), sqr(x1))) -> c17(A__ADD(recip(mark(z0)), a__sqr(mark(x1))), MARK(sqr(x1)))
   MARK(add(s(z0), sqr(x1))) -> c17(A__ADD(s(z0), a__sqr(mark(x1))), MARK(sqr(x1)))
   MARK(add(0, sqr(x1))) -> c17(A__ADD(0, a__sqr(mark(x1))), MARK(sqr(x1)))
   MARK(add(nil, sqr(x1))) -> c17(A__ADD(nil, a__sqr(mark(x1))), MARK(sqr(x1)))
   MARK(add(x0, sqr(x1))) -> c17(MARK(sqr(x1)))

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

(136)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2))))
   MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0))
   MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0))
   MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0))
   MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0))
   MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1))))
   MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0))
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   MARK(add(x0, terms(x1))) -> c17(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(terms(x1)))
   MARK(add(x0, terms(x1))) -> c17(A__ADD(mark(x0), terms(mark(x1))), MARK(terms(x1)))
   MARK(add(x0, terms(terms(z0)))) -> c17(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0))))
   MARK(add(x0, terms(sqr(z0)))) -> c17(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0))))
   MARK(add(x0, terms(add(z0, z1)))) -> c17(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1))))
   MARK(add(x0, terms(dbl(z0)))) -> c17(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0))))
   MARK(add(x0, terms(first(z0, z1)))) -> c17(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1))))
   MARK(add(x0, terms(cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1))))
   MARK(add(x0, terms(recip(z0)))) -> c17(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(terms(recip(z0))))
   MARK(add(x0, terms(s(z0)))) -> c17(A__ADD(mark(x0), a__terms(s(z0))), MARK(terms(s(z0))))
   MARK(add(x0, terms(0))) -> c17(A__ADD(mark(x0), a__terms(0)), MARK(terms(0)))
   MARK(add(x0, terms(nil))) -> c17(A__ADD(mark(x0), a__terms(nil)), MARK(terms(nil)))
   MARK(add(terms(z0), terms(x1))) -> c17(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(x1)))
   MARK(add(sqr(z0), terms(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(terms(x1)))
   MARK(add(add(z0, z1), terms(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(terms(x1)))
   MARK(add(dbl(z0), terms(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(terms(x1)))
   MARK(add(first(z0, z1), terms(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(terms(x1)))
   MARK(add(0, terms(x1))) -> c17(A__ADD(0, a__terms(mark(x1))), MARK(terms(x1)))
   MARK(add(x0, terms(x1))) -> c17(MARK(terms(x1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c17(MARK(terms(x1)))
   MARK(add(recip(z0), terms(x1))) -> c17(MARK(terms(x1)))
   MARK(add(s(z0), terms(x1))) -> c17(MARK(terms(x1)))
   MARK(add(nil, terms(x1))) -> c17(MARK(terms(x1)))
   MARK(add(x0, sqr(x1))) -> c17(A__ADD(mark(x0), sqr(mark(x1))), MARK(sqr(x1)))
   MARK(add(x0, sqr(terms(z0)))) -> c17(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0))))
   MARK(add(x0, sqr(sqr(z0)))) -> c17(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0))))
   MARK(add(x0, sqr(add(z0, z1)))) -> c17(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1))))
   MARK(add(x0, sqr(dbl(z0)))) -> c17(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0))))
   MARK(add(x0, sqr(first(z0, z1)))) -> c17(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1))))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1))))
   MARK(add(x0, sqr(recip(z0)))) -> c17(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0))))
   MARK(add(x0, sqr(s(z0)))) -> c17(A__ADD(mark(x0), a__sqr(s(z0))), MARK(sqr(s(z0))))
   MARK(add(x0, sqr(0))) -> c17(A__ADD(mark(x0), a__sqr(0)), MARK(sqr(0)))
   MARK(add(x0, sqr(nil))) -> c17(A__ADD(mark(x0), a__sqr(nil)), MARK(sqr(nil)))
   MARK(add(terms(z0), sqr(x1))) -> c17(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(sqr(x1)))
   MARK(add(sqr(z0), sqr(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(x1)))
   MARK(add(add(z0, z1), sqr(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(sqr(x1)))
   MARK(add(dbl(z0), sqr(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(sqr(x1)))
   MARK(add(first(z0, z1), sqr(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(sqr(x1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c17(A__ADD(cons(mark(z0), z1), a__sqr(mark(x1))), MARK(sqr(x1)))
   MARK(add(recip(z0), sqr(x1))) -> c17(A__ADD(recip(mark(z0)), a__sqr(mark(x1))), MARK(sqr(x1)))
   MARK(add(s(z0), sqr(x1))) -> c17(A__ADD(s(z0), a__sqr(mark(x1))), MARK(sqr(x1)))
   MARK(add(0, sqr(x1))) -> c17(A__ADD(0, a__sqr(mark(x1))), MARK(sqr(x1)))
   MARK(add(nil, sqr(x1))) -> c17(A__ADD(nil, a__sqr(mark(x1))), MARK(sqr(x1)))
   MARK(add(x0, sqr(x1))) -> c17(MARK(sqr(x1)))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
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   MARK(add(dbl(first(z0, z1)), x1)) -> c16(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(dbl(first(z0, z1))))
   MARK(add(dbl(cons(z0, z1)), x1)) -> c16(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(dbl(cons(z0, z1))))
   MARK(add(dbl(recip(z0)), x1)) -> c16(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(dbl(recip(z0))))
   MARK(add(dbl(s(z0)), x1)) -> c16(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(dbl(s(z0))))
   MARK(add(dbl(0), x1)) -> c16(A__ADD(a__dbl(0), mark(x1)), MARK(dbl(0)))
   MARK(add(dbl(nil), x1)) -> c16(A__ADD(a__dbl(nil), mark(x1)), MARK(dbl(nil)))
   MARK(add(dbl(x0), x1)) -> c16(MARK(dbl(x0)))
   MARK(add(first(x0, terms(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(first(x0, terms(z0))))
   MARK(add(first(x0, sqr(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(first(x0, sqr(z0))))
   MARK(add(first(x0, add(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, add(z0, z1))))
   MARK(add(first(x0, dbl(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(first(x0, dbl(z0))))
   MARK(add(first(x0, first(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1))))
   MARK(add(first(x0, cons(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1))))
   MARK(add(first(x0, recip(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), recip(mark(z0))), mark(x2)), MARK(first(x0, recip(z0))))
   MARK(add(first(x0, s(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(first(x0, s(z0))))
   MARK(add(first(x0, 0), x2)) -> c16(A__ADD(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0)))
   MARK(add(first(x0, nil), x2)) -> c16(A__ADD(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil)))
   MARK(add(first(terms(z0), x1), x2)) -> c16(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(first(terms(z0), x1)))
   MARK(add(first(sqr(z0), x1), x2)) -> c16(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(first(sqr(z0), x1)))
   MARK(add(first(add(z0, z1), x1), x2)) -> c16(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(add(z0, z1), x1)))
   MARK(add(first(dbl(z0), x1), x2)) -> c16(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(first(dbl(z0), x1)))
   MARK(add(first(first(z0, z1), x1), x2)) -> c16(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1)))
   MARK(add(first(cons(z0, z1), x1), x2)) -> c16(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1)))
   MARK(add(first(recip(z0), x1), x2)) -> c16(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(first(recip(z0), x1)))
   MARK(add(first(s(z0), x1), x2)) -> c16(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(first(s(z0), x1)))
   MARK(add(first(0, x1), x2)) -> c16(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1)))
   MARK(add(first(nil, x1), x2)) -> c16(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1)))
   MARK(add(first(x0, x1), x2)) -> c16(MARK(first(x0, x1)))
   MARK(add(x0, terms(x1))) -> c17(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(terms(x1)))
   MARK(add(x0, terms(x1))) -> c17(A__ADD(mark(x0), terms(mark(x1))), MARK(terms(x1)))
   MARK(add(x0, terms(terms(z0)))) -> c17(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0))))
   MARK(add(x0, terms(sqr(z0)))) -> c17(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0))))
   MARK(add(x0, terms(add(z0, z1)))) -> c17(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1))))
   MARK(add(x0, terms(dbl(z0)))) -> c17(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0))))
   MARK(add(x0, terms(first(z0, z1)))) -> c17(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1))))
   MARK(add(x0, terms(cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1))))
   MARK(add(x0, terms(recip(z0)))) -> c17(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(terms(recip(z0))))
   MARK(add(x0, terms(s(z0)))) -> c17(A__ADD(mark(x0), a__terms(s(z0))), MARK(terms(s(z0))))
   MARK(add(x0, terms(0))) -> c17(A__ADD(mark(x0), a__terms(0)), MARK(terms(0)))
   MARK(add(x0, terms(nil))) -> c17(A__ADD(mark(x0), a__terms(nil)), MARK(terms(nil)))
   MARK(add(terms(z0), terms(x1))) -> c17(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(x1)))
   MARK(add(sqr(z0), terms(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(terms(x1)))
   MARK(add(add(z0, z1), terms(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(terms(x1)))
   MARK(add(dbl(z0), terms(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(terms(x1)))
   MARK(add(first(z0, z1), terms(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(terms(x1)))
   MARK(add(0, terms(x1))) -> c17(A__ADD(0, a__terms(mark(x1))), MARK(terms(x1)))
   MARK(add(x0, terms(x1))) -> c17(MARK(terms(x1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c17(MARK(terms(x1)))
   MARK(add(recip(z0), terms(x1))) -> c17(MARK(terms(x1)))
   MARK(add(s(z0), terms(x1))) -> c17(MARK(terms(x1)))
   MARK(add(nil, terms(x1))) -> c17(MARK(terms(x1)))
   MARK(add(x0, sqr(x1))) -> c17(A__ADD(mark(x0), sqr(mark(x1))), MARK(sqr(x1)))
   MARK(add(x0, sqr(terms(z0)))) -> c17(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0))))
   MARK(add(x0, sqr(sqr(z0)))) -> c17(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0))))
   MARK(add(x0, sqr(add(z0, z1)))) -> c17(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1))))
   MARK(add(x0, sqr(dbl(z0)))) -> c17(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0))))
   MARK(add(x0, sqr(first(z0, z1)))) -> c17(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1))))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1))))
   MARK(add(x0, sqr(recip(z0)))) -> c17(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0))))
   MARK(add(x0, sqr(s(z0)))) -> c17(A__ADD(mark(x0), a__sqr(s(z0))), MARK(sqr(s(z0))))
   MARK(add(x0, sqr(0))) -> c17(A__ADD(mark(x0), a__sqr(0)), MARK(sqr(0)))
   MARK(add(x0, sqr(nil))) -> c17(A__ADD(mark(x0), a__sqr(nil)), MARK(sqr(nil)))
   MARK(add(terms(z0), sqr(x1))) -> c17(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(sqr(x1)))
   MARK(add(sqr(z0), sqr(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(x1)))
   MARK(add(add(z0, z1), sqr(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(sqr(x1)))
   MARK(add(dbl(z0), sqr(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(sqr(x1)))
   MARK(add(first(z0, z1), sqr(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(sqr(x1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c17(A__ADD(cons(mark(z0), z1), a__sqr(mark(x1))), MARK(sqr(x1)))
   MARK(add(recip(z0), sqr(x1))) -> c17(A__ADD(recip(mark(z0)), a__sqr(mark(x1))), MARK(sqr(x1)))
   MARK(add(s(z0), sqr(x1))) -> c17(A__ADD(s(z0), a__sqr(mark(x1))), MARK(sqr(x1)))
   MARK(add(0, sqr(x1))) -> c17(A__ADD(0, a__sqr(mark(x1))), MARK(sqr(x1)))
   MARK(add(nil, sqr(x1))) -> c17(A__ADD(nil, a__sqr(mark(x1))), MARK(sqr(x1)))
   MARK(add(x0, sqr(x1))) -> c17(MARK(sqr(x1)))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2


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

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

(138)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
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   MARK(add(terms(cons(z0, z1)), x1)) -> c16(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(terms(cons(z0, z1))))
   MARK(add(terms(recip(z0)), x1)) -> c16(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(terms(recip(z0))))
   MARK(add(terms(s(z0)), x1)) -> c16(A__ADD(a__terms(s(z0)), mark(x1)), MARK(terms(s(z0))))
   MARK(add(terms(0), x1)) -> c16(A__ADD(a__terms(0), mark(x1)), MARK(terms(0)))
   MARK(add(terms(nil), x1)) -> c16(A__ADD(a__terms(nil), mark(x1)), MARK(terms(nil)))
   MARK(add(terms(x0), x1)) -> c16(MARK(terms(x0)))
   MARK(add(sqr(terms(z0)), x1)) -> c16(A__ADD(a__sqr(a__terms(mark(z0))), mark(x1)), MARK(sqr(terms(z0))))
   MARK(add(sqr(sqr(z0)), x1)) -> c16(A__ADD(a__sqr(a__sqr(mark(z0))), mark(x1)), MARK(sqr(sqr(z0))))
   MARK(add(sqr(add(z0, z1)), x1)) -> c16(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), mark(x1)), MARK(sqr(add(z0, z1))))
   MARK(add(sqr(dbl(z0)), x1)) -> c16(A__ADD(a__sqr(a__dbl(mark(z0))), mark(x1)), MARK(sqr(dbl(z0))))
   MARK(add(sqr(first(z0, z1)), x1)) -> c16(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), mark(x1)), MARK(sqr(first(z0, z1))))
   MARK(add(sqr(cons(z0, z1)), x1)) -> c16(A__ADD(a__sqr(cons(mark(z0), z1)), mark(x1)), MARK(sqr(cons(z0, z1))))
   MARK(add(sqr(recip(z0)), x1)) -> c16(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(sqr(recip(z0))))
   MARK(add(sqr(s(z0)), x1)) -> c16(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(sqr(s(z0))))
   MARK(add(sqr(0), x1)) -> c16(A__ADD(a__sqr(0), mark(x1)), MARK(sqr(0)))
   MARK(add(sqr(nil), x1)) -> c16(A__ADD(a__sqr(nil), mark(x1)), MARK(sqr(nil)))
   MARK(add(sqr(x0), x1)) -> c16(MARK(sqr(x0)))
   MARK(add(add(x0, terms(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(add(x0, terms(z0))))
   MARK(add(add(x0, sqr(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(add(x0, sqr(z0))))
   MARK(add(add(x0, add(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, add(z0, z1))))
   MARK(add(add(x0, dbl(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(add(x0, dbl(z0))))
   MARK(add(add(x0, first(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, first(z0, z1))))
   MARK(add(add(x0, cons(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(add(x0, cons(z0, z1))))
   MARK(add(add(x0, recip(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), recip(mark(z0))), mark(x2)), MARK(add(x0, recip(z0))))
   MARK(add(add(x0, s(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), s(z0)), mark(x2)), MARK(add(x0, s(z0))))
   MARK(add(add(x0, 0), x2)) -> c16(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(add(x0, 0)))
   MARK(add(add(x0, nil), x2)) -> c16(A__ADD(a__add(mark(x0), nil), mark(x2)), MARK(add(x0, nil)))
   MARK(add(add(terms(z0), x1), x2)) -> c16(A__ADD(a__add(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(add(terms(z0), x1)))
   MARK(add(add(sqr(z0), x1), x2)) -> c16(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(add(sqr(z0), x1)))
   MARK(add(add(add(z0, z1), x1), x2)) -> c16(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(add(z0, z1), x1)))
   MARK(add(add(dbl(z0), x1), x2)) -> c16(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(add(dbl(z0), x1)))
   MARK(add(add(first(z0, z1), x1), x2)) -> c16(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(first(z0, z1), x1)))
   MARK(add(add(cons(z0, z1), x1), x2)) -> c16(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(add(cons(z0, z1), x1)))
   MARK(add(add(recip(z0), x1), x2)) -> c16(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(add(recip(z0), x1)))
   MARK(add(add(s(z0), x1), x2)) -> c16(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(add(s(z0), x1)))
   MARK(add(add(0, x1), x2)) -> c16(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(add(0, x1)))
   MARK(add(add(nil, x1), x2)) -> c16(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(add(nil, x1)))
   MARK(add(add(x0, x1), x2)) -> c16(MARK(add(x0, x1)))
   MARK(add(dbl(terms(z0)), x1)) -> c16(A__ADD(a__dbl(a__terms(mark(z0))), mark(x1)), MARK(dbl(terms(z0))))
   MARK(add(dbl(sqr(z0)), x1)) -> c16(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(dbl(sqr(z0))))
   MARK(add(dbl(add(z0, z1)), x1)) -> c16(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(dbl(add(z0, z1))))
   MARK(add(dbl(dbl(z0)), x1)) -> c16(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(dbl(dbl(z0))))
   MARK(add(dbl(first(z0, z1)), x1)) -> c16(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(dbl(first(z0, z1))))
   MARK(add(dbl(cons(z0, z1)), x1)) -> c16(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(dbl(cons(z0, z1))))
   MARK(add(dbl(recip(z0)), x1)) -> c16(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(dbl(recip(z0))))
   MARK(add(dbl(s(z0)), x1)) -> c16(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(dbl(s(z0))))
   MARK(add(dbl(0), x1)) -> c16(A__ADD(a__dbl(0), mark(x1)), MARK(dbl(0)))
   MARK(add(dbl(nil), x1)) -> c16(A__ADD(a__dbl(nil), mark(x1)), MARK(dbl(nil)))
   MARK(add(dbl(x0), x1)) -> c16(MARK(dbl(x0)))
   MARK(add(first(x0, terms(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(first(x0, terms(z0))))
   MARK(add(first(x0, sqr(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(first(x0, sqr(z0))))
   MARK(add(first(x0, add(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, add(z0, z1))))
   MARK(add(first(x0, dbl(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(first(x0, dbl(z0))))
   MARK(add(first(x0, first(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1))))
   MARK(add(first(x0, cons(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1))))
   MARK(add(first(x0, recip(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), recip(mark(z0))), mark(x2)), MARK(first(x0, recip(z0))))
   MARK(add(first(x0, s(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(first(x0, s(z0))))
   MARK(add(first(x0, 0), x2)) -> c16(A__ADD(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0)))
   MARK(add(first(x0, nil), x2)) -> c16(A__ADD(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil)))
   MARK(add(first(terms(z0), x1), x2)) -> c16(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(first(terms(z0), x1)))
   MARK(add(first(sqr(z0), x1), x2)) -> c16(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(first(sqr(z0), x1)))
   MARK(add(first(add(z0, z1), x1), x2)) -> c16(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(add(z0, z1), x1)))
   MARK(add(first(dbl(z0), x1), x2)) -> c16(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(first(dbl(z0), x1)))
   MARK(add(first(first(z0, z1), x1), x2)) -> c16(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1)))
   MARK(add(first(cons(z0, z1), x1), x2)) -> c16(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1)))
   MARK(add(first(recip(z0), x1), x2)) -> c16(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(first(recip(z0), x1)))
   MARK(add(first(s(z0), x1), x2)) -> c16(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(first(s(z0), x1)))
   MARK(add(first(0, x1), x2)) -> c16(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1)))
   MARK(add(first(nil, x1), x2)) -> c16(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1)))
   MARK(add(first(x0, x1), x2)) -> c16(MARK(first(x0, x1)))
   MARK(add(x0, terms(x1))) -> c17(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(terms(x1)))
   MARK(add(x0, terms(x1))) -> c17(A__ADD(mark(x0), terms(mark(x1))), MARK(terms(x1)))
   MARK(add(x0, terms(terms(z0)))) -> c17(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0))))
   MARK(add(x0, terms(sqr(z0)))) -> c17(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0))))
   MARK(add(x0, terms(add(z0, z1)))) -> c17(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1))))
   MARK(add(x0, terms(dbl(z0)))) -> c17(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0))))
   MARK(add(x0, terms(first(z0, z1)))) -> c17(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1))))
   MARK(add(x0, terms(cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1))))
   MARK(add(x0, terms(recip(z0)))) -> c17(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(terms(recip(z0))))
   MARK(add(x0, terms(s(z0)))) -> c17(A__ADD(mark(x0), a__terms(s(z0))), MARK(terms(s(z0))))
   MARK(add(x0, terms(0))) -> c17(A__ADD(mark(x0), a__terms(0)), MARK(terms(0)))
   MARK(add(x0, terms(nil))) -> c17(A__ADD(mark(x0), a__terms(nil)), MARK(terms(nil)))
   MARK(add(terms(z0), terms(x1))) -> c17(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(x1)))
   MARK(add(sqr(z0), terms(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(terms(x1)))
   MARK(add(add(z0, z1), terms(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(terms(x1)))
   MARK(add(dbl(z0), terms(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(terms(x1)))
   MARK(add(first(z0, z1), terms(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(terms(x1)))
   MARK(add(0, terms(x1))) -> c17(A__ADD(0, a__terms(mark(x1))), MARK(terms(x1)))
   MARK(add(x0, terms(x1))) -> c17(MARK(terms(x1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c17(MARK(terms(x1)))
   MARK(add(recip(z0), terms(x1))) -> c17(MARK(terms(x1)))
   MARK(add(s(z0), terms(x1))) -> c17(MARK(terms(x1)))
   MARK(add(nil, terms(x1))) -> c17(MARK(terms(x1)))
   MARK(add(x0, sqr(x1))) -> c17(A__ADD(mark(x0), sqr(mark(x1))), MARK(sqr(x1)))
   MARK(add(x0, sqr(terms(z0)))) -> c17(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0))))
   MARK(add(x0, sqr(sqr(z0)))) -> c17(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0))))
   MARK(add(x0, sqr(add(z0, z1)))) -> c17(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1))))
   MARK(add(x0, sqr(dbl(z0)))) -> c17(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0))))
   MARK(add(x0, sqr(first(z0, z1)))) -> c17(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1))))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1))))
   MARK(add(x0, sqr(recip(z0)))) -> c17(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0))))
   MARK(add(x0, sqr(s(z0)))) -> c17(A__ADD(mark(x0), a__sqr(s(z0))), MARK(sqr(s(z0))))
   MARK(add(x0, sqr(0))) -> c17(A__ADD(mark(x0), a__sqr(0)), MARK(sqr(0)))
   MARK(add(x0, sqr(nil))) -> c17(A__ADD(mark(x0), a__sqr(nil)), MARK(sqr(nil)))
   MARK(add(terms(z0), sqr(x1))) -> c17(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(sqr(x1)))
   MARK(add(sqr(z0), sqr(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(x1)))
   MARK(add(add(z0, z1), sqr(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(sqr(x1)))
   MARK(add(dbl(z0), sqr(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(sqr(x1)))
   MARK(add(first(z0, z1), sqr(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(sqr(x1)))
   MARK(add(0, sqr(x1))) -> c17(A__ADD(0, a__sqr(mark(x1))), MARK(sqr(x1)))
   MARK(add(x0, sqr(x1))) -> c17(MARK(sqr(x1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c17(MARK(sqr(x1)))
   MARK(add(recip(z0), sqr(x1))) -> c17(MARK(sqr(x1)))
   MARK(add(s(z0), sqr(x1))) -> c17(MARK(sqr(x1)))
   MARK(add(nil, sqr(x1))) -> c17(MARK(sqr(x1)))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
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   MARK(add(sqr(z0), recip(x1))) -> c16(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), recip(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), recip(x1))) -> c16(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), recip(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), recip(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), recip(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, recip(x1))) -> c16(A__ADD(0, recip(mark(x1))))
   MARK(add(terms(z0), s(x1))) -> c16(A__ADD(a__terms(mark(z0)), s(x1)), MARK(terms(z0)))
   MARK(add(sqr(z0), s(x1))) -> c16(A__ADD(a__sqr(mark(z0)), s(x1)), MARK(sqr(z0)))
   MARK(add(add(z0, z1), s(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), s(x1)), MARK(add(z0, z1)))
   MARK(add(dbl(z0), s(x1))) -> c16(A__ADD(a__dbl(mark(z0)), s(x1)), MARK(dbl(z0)))
   MARK(add(first(z0, z1), s(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), s(x1)), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), s(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), s(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, s(x1))) -> c16(A__ADD(0, s(x1)))
   MARK(add(terms(z0), 0)) -> c16(A__ADD(a__terms(mark(z0)), 0), MARK(terms(z0)))
   MARK(add(sqr(z0), 0)) -> c16(A__ADD(a__sqr(mark(z0)), 0), MARK(sqr(z0)))
   MARK(add(add(z0, z1), 0)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1)))
   MARK(add(dbl(z0), 0)) -> c16(A__ADD(a__dbl(mark(z0)), 0), MARK(dbl(z0)))
   MARK(add(first(z0, z1), 0)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), 0), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), 0)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), 0)) -> c16(MARK(recip(z0)))
   MARK(add(0, 0)) -> c16(A__ADD(0, 0))
   MARK(add(terms(z0), nil)) -> c16(A__ADD(a__terms(mark(z0)), nil), MARK(terms(z0)))
   MARK(add(sqr(z0), nil)) -> c16(A__ADD(a__sqr(mark(z0)), nil), MARK(sqr(z0)))
   MARK(add(add(z0, z1), nil)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), nil), MARK(add(z0, z1)))
   MARK(add(dbl(z0), nil)) -> c16(A__ADD(a__dbl(mark(z0)), nil), MARK(dbl(z0)))
   MARK(add(first(z0, z1), nil)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), nil), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), nil)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), nil)) -> c16(MARK(recip(z0)))
   MARK(add(0, nil)) -> c16(A__ADD(0, nil))
   MARK(add(terms(terms(z0)), x1)) -> c16(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(terms(terms(z0))))
   MARK(add(terms(sqr(z0)), x1)) -> c16(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(terms(sqr(z0))))
   MARK(add(terms(add(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(terms(add(z0, z1))))
   MARK(add(terms(dbl(z0)), x1)) -> c16(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(terms(dbl(z0))))
   MARK(add(terms(first(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(terms(first(z0, z1))))
   MARK(add(terms(cons(z0, z1)), x1)) -> c16(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(terms(cons(z0, z1))))
   MARK(add(terms(recip(z0)), x1)) -> c16(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(terms(recip(z0))))
   MARK(add(terms(s(z0)), x1)) -> c16(A__ADD(a__terms(s(z0)), mark(x1)), MARK(terms(s(z0))))
   MARK(add(terms(0), x1)) -> c16(A__ADD(a__terms(0), mark(x1)), MARK(terms(0)))
   MARK(add(terms(nil), x1)) -> c16(A__ADD(a__terms(nil), mark(x1)), MARK(terms(nil)))
   MARK(add(terms(x0), x1)) -> c16(MARK(terms(x0)))
   MARK(add(sqr(terms(z0)), x1)) -> c16(A__ADD(a__sqr(a__terms(mark(z0))), mark(x1)), MARK(sqr(terms(z0))))
   MARK(add(sqr(sqr(z0)), x1)) -> c16(A__ADD(a__sqr(a__sqr(mark(z0))), mark(x1)), MARK(sqr(sqr(z0))))
   MARK(add(sqr(add(z0, z1)), x1)) -> c16(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), mark(x1)), MARK(sqr(add(z0, z1))))
   MARK(add(sqr(dbl(z0)), x1)) -> c16(A__ADD(a__sqr(a__dbl(mark(z0))), mark(x1)), MARK(sqr(dbl(z0))))
   MARK(add(sqr(first(z0, z1)), x1)) -> c16(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), mark(x1)), MARK(sqr(first(z0, z1))))
   MARK(add(sqr(cons(z0, z1)), x1)) -> c16(A__ADD(a__sqr(cons(mark(z0), z1)), mark(x1)), MARK(sqr(cons(z0, z1))))
   MARK(add(sqr(recip(z0)), x1)) -> c16(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(sqr(recip(z0))))
   MARK(add(sqr(s(z0)), x1)) -> c16(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(sqr(s(z0))))
   MARK(add(sqr(0), x1)) -> c16(A__ADD(a__sqr(0), mark(x1)), MARK(sqr(0)))
   MARK(add(sqr(nil), x1)) -> c16(A__ADD(a__sqr(nil), mark(x1)), MARK(sqr(nil)))
   MARK(add(sqr(x0), x1)) -> c16(MARK(sqr(x0)))
   MARK(add(add(x0, terms(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(add(x0, terms(z0))))
   MARK(add(add(x0, sqr(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(add(x0, sqr(z0))))
   MARK(add(add(x0, add(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, add(z0, z1))))
   MARK(add(add(x0, dbl(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(add(x0, dbl(z0))))
   MARK(add(add(x0, first(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, first(z0, z1))))
   MARK(add(add(x0, cons(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(add(x0, cons(z0, z1))))
   MARK(add(add(x0, recip(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), recip(mark(z0))), mark(x2)), MARK(add(x0, recip(z0))))
   MARK(add(add(x0, s(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), s(z0)), mark(x2)), MARK(add(x0, s(z0))))
   MARK(add(add(x0, 0), x2)) -> c16(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(add(x0, 0)))
   MARK(add(add(x0, nil), x2)) -> c16(A__ADD(a__add(mark(x0), nil), mark(x2)), MARK(add(x0, nil)))
   MARK(add(add(terms(z0), x1), x2)) -> c16(A__ADD(a__add(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(add(terms(z0), x1)))
   MARK(add(add(sqr(z0), x1), x2)) -> c16(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(add(sqr(z0), x1)))
   MARK(add(add(add(z0, z1), x1), x2)) -> c16(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(add(z0, z1), x1)))
   MARK(add(add(dbl(z0), x1), x2)) -> c16(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(add(dbl(z0), x1)))
   MARK(add(add(first(z0, z1), x1), x2)) -> c16(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(first(z0, z1), x1)))
   MARK(add(add(cons(z0, z1), x1), x2)) -> c16(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(add(cons(z0, z1), x1)))
   MARK(add(add(recip(z0), x1), x2)) -> c16(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(add(recip(z0), x1)))
   MARK(add(add(s(z0), x1), x2)) -> c16(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(add(s(z0), x1)))
   MARK(add(add(0, x1), x2)) -> c16(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(add(0, x1)))
   MARK(add(add(nil, x1), x2)) -> c16(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(add(nil, x1)))
   MARK(add(add(x0, x1), x2)) -> c16(MARK(add(x0, x1)))
   MARK(add(dbl(terms(z0)), x1)) -> c16(A__ADD(a__dbl(a__terms(mark(z0))), mark(x1)), MARK(dbl(terms(z0))))
   MARK(add(dbl(sqr(z0)), x1)) -> c16(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(dbl(sqr(z0))))
   MARK(add(dbl(add(z0, z1)), x1)) -> c16(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(dbl(add(z0, z1))))
   MARK(add(dbl(dbl(z0)), x1)) -> c16(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(dbl(dbl(z0))))
   MARK(add(dbl(first(z0, z1)), x1)) -> c16(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(dbl(first(z0, z1))))
   MARK(add(dbl(cons(z0, z1)), x1)) -> c16(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(dbl(cons(z0, z1))))
   MARK(add(dbl(recip(z0)), x1)) -> c16(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(dbl(recip(z0))))
   MARK(add(dbl(s(z0)), x1)) -> c16(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(dbl(s(z0))))
   MARK(add(dbl(0), x1)) -> c16(A__ADD(a__dbl(0), mark(x1)), MARK(dbl(0)))
   MARK(add(dbl(nil), x1)) -> c16(A__ADD(a__dbl(nil), mark(x1)), MARK(dbl(nil)))
   MARK(add(dbl(x0), x1)) -> c16(MARK(dbl(x0)))
   MARK(add(first(x0, terms(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(first(x0, terms(z0))))
   MARK(add(first(x0, sqr(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(first(x0, sqr(z0))))
   MARK(add(first(x0, add(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, add(z0, z1))))
   MARK(add(first(x0, dbl(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(first(x0, dbl(z0))))
   MARK(add(first(x0, first(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1))))
   MARK(add(first(x0, cons(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1))))
   MARK(add(first(x0, recip(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), recip(mark(z0))), mark(x2)), MARK(first(x0, recip(z0))))
   MARK(add(first(x0, s(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(first(x0, s(z0))))
   MARK(add(first(x0, 0), x2)) -> c16(A__ADD(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0)))
   MARK(add(first(x0, nil), x2)) -> c16(A__ADD(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil)))
   MARK(add(first(terms(z0), x1), x2)) -> c16(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(first(terms(z0), x1)))
   MARK(add(first(sqr(z0), x1), x2)) -> c16(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(first(sqr(z0), x1)))
   MARK(add(first(add(z0, z1), x1), x2)) -> c16(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(add(z0, z1), x1)))
   MARK(add(first(dbl(z0), x1), x2)) -> c16(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(first(dbl(z0), x1)))
   MARK(add(first(first(z0, z1), x1), x2)) -> c16(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1)))
   MARK(add(first(cons(z0, z1), x1), x2)) -> c16(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1)))
   MARK(add(first(recip(z0), x1), x2)) -> c16(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(first(recip(z0), x1)))
   MARK(add(first(s(z0), x1), x2)) -> c16(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(first(s(z0), x1)))
   MARK(add(first(0, x1), x2)) -> c16(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1)))
   MARK(add(first(nil, x1), x2)) -> c16(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1)))
   MARK(add(first(x0, x1), x2)) -> c16(MARK(first(x0, x1)))
   MARK(add(x0, terms(x1))) -> c17(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(terms(x1)))
   MARK(add(x0, terms(x1))) -> c17(A__ADD(mark(x0), terms(mark(x1))), MARK(terms(x1)))
   MARK(add(x0, terms(terms(z0)))) -> c17(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0))))
   MARK(add(x0, terms(sqr(z0)))) -> c17(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0))))
   MARK(add(x0, terms(add(z0, z1)))) -> c17(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1))))
   MARK(add(x0, terms(dbl(z0)))) -> c17(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0))))
   MARK(add(x0, terms(first(z0, z1)))) -> c17(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1))))
   MARK(add(x0, terms(cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1))))
   MARK(add(x0, terms(recip(z0)))) -> c17(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(terms(recip(z0))))
   MARK(add(x0, terms(s(z0)))) -> c17(A__ADD(mark(x0), a__terms(s(z0))), MARK(terms(s(z0))))
   MARK(add(x0, terms(0))) -> c17(A__ADD(mark(x0), a__terms(0)), MARK(terms(0)))
   MARK(add(x0, terms(nil))) -> c17(A__ADD(mark(x0), a__terms(nil)), MARK(terms(nil)))
   MARK(add(terms(z0), terms(x1))) -> c17(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(x1)))
   MARK(add(sqr(z0), terms(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(terms(x1)))
   MARK(add(add(z0, z1), terms(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(terms(x1)))
   MARK(add(dbl(z0), terms(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(terms(x1)))
   MARK(add(first(z0, z1), terms(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(terms(x1)))
   MARK(add(0, terms(x1))) -> c17(A__ADD(0, a__terms(mark(x1))), MARK(terms(x1)))
   MARK(add(x0, terms(x1))) -> c17(MARK(terms(x1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c17(MARK(terms(x1)))
   MARK(add(recip(z0), terms(x1))) -> c17(MARK(terms(x1)))
   MARK(add(s(z0), terms(x1))) -> c17(MARK(terms(x1)))
   MARK(add(nil, terms(x1))) -> c17(MARK(terms(x1)))
   MARK(add(x0, sqr(x1))) -> c17(A__ADD(mark(x0), sqr(mark(x1))), MARK(sqr(x1)))
   MARK(add(x0, sqr(terms(z0)))) -> c17(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0))))
   MARK(add(x0, sqr(sqr(z0)))) -> c17(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0))))
   MARK(add(x0, sqr(add(z0, z1)))) -> c17(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1))))
   MARK(add(x0, sqr(dbl(z0)))) -> c17(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0))))
   MARK(add(x0, sqr(first(z0, z1)))) -> c17(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1))))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1))))
   MARK(add(x0, sqr(recip(z0)))) -> c17(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0))))
   MARK(add(x0, sqr(s(z0)))) -> c17(A__ADD(mark(x0), a__sqr(s(z0))), MARK(sqr(s(z0))))
   MARK(add(x0, sqr(0))) -> c17(A__ADD(mark(x0), a__sqr(0)), MARK(sqr(0)))
   MARK(add(x0, sqr(nil))) -> c17(A__ADD(mark(x0), a__sqr(nil)), MARK(sqr(nil)))
   MARK(add(terms(z0), sqr(x1))) -> c17(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(sqr(x1)))
   MARK(add(sqr(z0), sqr(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(x1)))
   MARK(add(add(z0, z1), sqr(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(sqr(x1)))
   MARK(add(dbl(z0), sqr(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(sqr(x1)))
   MARK(add(first(z0, z1), sqr(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(sqr(x1)))
   MARK(add(0, sqr(x1))) -> c17(A__ADD(0, a__sqr(mark(x1))), MARK(sqr(x1)))
   MARK(add(x0, sqr(x1))) -> c17(MARK(sqr(x1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c17(MARK(sqr(x1)))
   MARK(add(recip(z0), sqr(x1))) -> c17(MARK(sqr(x1)))
   MARK(add(s(z0), sqr(x1))) -> c17(MARK(sqr(x1)))
   MARK(add(nil, sqr(x1))) -> c17(MARK(sqr(x1)))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2


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

(139) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) by 
   MARK(add(x0, add(x1, x2))) -> c17(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(add(x1, x2)))
   MARK(add(x0, add(x1, terms(z0)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(add(x1, terms(z0))))
   MARK(add(x0, add(x1, sqr(z0)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(add(x1, sqr(z0))))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(add(x1, add(z0, z1))))
   MARK(add(x0, add(x1, dbl(z0)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(add(x1, dbl(z0))))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(add(x1, first(z0, z1))))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(add(x1, cons(z0, z1))))
   MARK(add(x0, add(x1, recip(z0)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(add(x1, recip(z0))))
   MARK(add(x0, add(x1, s(z0)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(add(x1, s(z0))))
   MARK(add(x0, add(x1, 0))) -> c17(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(add(x1, 0)))
   MARK(add(x0, add(x1, nil))) -> c17(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(add(x1, nil)))
   MARK(add(x0, add(terms(z0), x2))) -> c17(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(add(terms(z0), x2)))
   MARK(add(x0, add(sqr(z0), x2))) -> c17(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(add(sqr(z0), x2)))
   MARK(add(x0, add(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(add(add(z0, z1), x2)))
   MARK(add(x0, add(dbl(z0), x2))) -> c17(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(add(dbl(z0), x2)))
   MARK(add(x0, add(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(add(first(z0, z1), x2)))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(add(cons(z0, z1), x2)))
   MARK(add(x0, add(recip(z0), x2))) -> c17(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(add(recip(z0), x2)))
   MARK(add(x0, add(s(z0), x2))) -> c17(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(add(s(z0), x2)))
   MARK(add(x0, add(0, x2))) -> c17(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(add(0, x2)))
   MARK(add(x0, add(nil, x2))) -> c17(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(add(nil, x2)))
   MARK(add(terms(z0), add(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2)))
   MARK(add(sqr(z0), add(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2)))
   MARK(add(add(z0, z1), add(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2)))
   MARK(add(dbl(z0), add(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2)))
   MARK(add(first(z0, z1), add(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2)))
   MARK(add(cons(z0, z1), add(x1, x2))) -> c17(A__ADD(cons(mark(z0), z1), a__add(mark(x1), mark(x2))), MARK(add(x1, x2)))
   MARK(add(recip(z0), add(x1, x2))) -> c17(A__ADD(recip(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2)))
   MARK(add(s(z0), add(x1, x2))) -> c17(A__ADD(s(z0), a__add(mark(x1), mark(x2))), MARK(add(x1, x2)))
   MARK(add(0, add(x1, x2))) -> c17(A__ADD(0, a__add(mark(x1), mark(x2))), MARK(add(x1, x2)))
   MARK(add(nil, add(x1, x2))) -> c17(A__ADD(nil, a__add(mark(x1), mark(x2))), MARK(add(x1, x2)))

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

(140)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
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   MARK(add(dbl(sqr(z0)), x1)) -> c16(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(dbl(sqr(z0))))
   MARK(add(dbl(add(z0, z1)), x1)) -> c16(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(dbl(add(z0, z1))))
   MARK(add(dbl(dbl(z0)), x1)) -> c16(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(dbl(dbl(z0))))
   MARK(add(dbl(first(z0, z1)), x1)) -> c16(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(dbl(first(z0, z1))))
   MARK(add(dbl(cons(z0, z1)), x1)) -> c16(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(dbl(cons(z0, z1))))
   MARK(add(dbl(recip(z0)), x1)) -> c16(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(dbl(recip(z0))))
   MARK(add(dbl(s(z0)), x1)) -> c16(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(dbl(s(z0))))
   MARK(add(dbl(0), x1)) -> c16(A__ADD(a__dbl(0), mark(x1)), MARK(dbl(0)))
   MARK(add(dbl(nil), x1)) -> c16(A__ADD(a__dbl(nil), mark(x1)), MARK(dbl(nil)))
   MARK(add(dbl(x0), x1)) -> c16(MARK(dbl(x0)))
   MARK(add(first(x0, terms(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(first(x0, terms(z0))))
   MARK(add(first(x0, sqr(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(first(x0, sqr(z0))))
   MARK(add(first(x0, add(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, add(z0, z1))))
   MARK(add(first(x0, dbl(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(first(x0, dbl(z0))))
   MARK(add(first(x0, first(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1))))
   MARK(add(first(x0, cons(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1))))
   MARK(add(first(x0, recip(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), recip(mark(z0))), mark(x2)), MARK(first(x0, recip(z0))))
   MARK(add(first(x0, s(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(first(x0, s(z0))))
   MARK(add(first(x0, 0), x2)) -> c16(A__ADD(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0)))
   MARK(add(first(x0, nil), x2)) -> c16(A__ADD(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil)))
   MARK(add(first(terms(z0), x1), x2)) -> c16(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(first(terms(z0), x1)))
   MARK(add(first(sqr(z0), x1), x2)) -> c16(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(first(sqr(z0), x1)))
   MARK(add(first(add(z0, z1), x1), x2)) -> c16(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(add(z0, z1), x1)))
   MARK(add(first(dbl(z0), x1), x2)) -> c16(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(first(dbl(z0), x1)))
   MARK(add(first(first(z0, z1), x1), x2)) -> c16(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1)))
   MARK(add(first(cons(z0, z1), x1), x2)) -> c16(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1)))
   MARK(add(first(recip(z0), x1), x2)) -> c16(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(first(recip(z0), x1)))
   MARK(add(first(s(z0), x1), x2)) -> c16(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(first(s(z0), x1)))
   MARK(add(first(0, x1), x2)) -> c16(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1)))
   MARK(add(first(nil, x1), x2)) -> c16(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1)))
   MARK(add(first(x0, x1), x2)) -> c16(MARK(first(x0, x1)))
   MARK(add(x0, terms(x1))) -> c17(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(terms(x1)))
   MARK(add(x0, terms(x1))) -> c17(A__ADD(mark(x0), terms(mark(x1))), MARK(terms(x1)))
   MARK(add(x0, terms(terms(z0)))) -> c17(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0))))
   MARK(add(x0, terms(sqr(z0)))) -> c17(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0))))
   MARK(add(x0, terms(add(z0, z1)))) -> c17(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1))))
   MARK(add(x0, terms(dbl(z0)))) -> c17(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0))))
   MARK(add(x0, terms(first(z0, z1)))) -> c17(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1))))
   MARK(add(x0, terms(cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1))))
   MARK(add(x0, terms(recip(z0)))) -> c17(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(terms(recip(z0))))
   MARK(add(x0, terms(s(z0)))) -> c17(A__ADD(mark(x0), a__terms(s(z0))), MARK(terms(s(z0))))
   MARK(add(x0, terms(0))) -> c17(A__ADD(mark(x0), a__terms(0)), MARK(terms(0)))
   MARK(add(x0, terms(nil))) -> c17(A__ADD(mark(x0), a__terms(nil)), MARK(terms(nil)))
   MARK(add(terms(z0), terms(x1))) -> c17(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(x1)))
   MARK(add(sqr(z0), terms(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(terms(x1)))
   MARK(add(add(z0, z1), terms(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(terms(x1)))
   MARK(add(dbl(z0), terms(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(terms(x1)))
   MARK(add(first(z0, z1), terms(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(terms(x1)))
   MARK(add(0, terms(x1))) -> c17(A__ADD(0, a__terms(mark(x1))), MARK(terms(x1)))
   MARK(add(x0, terms(x1))) -> c17(MARK(terms(x1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c17(MARK(terms(x1)))
   MARK(add(recip(z0), terms(x1))) -> c17(MARK(terms(x1)))
   MARK(add(s(z0), terms(x1))) -> c17(MARK(terms(x1)))
   MARK(add(nil, terms(x1))) -> c17(MARK(terms(x1)))
   MARK(add(x0, sqr(x1))) -> c17(A__ADD(mark(x0), sqr(mark(x1))), MARK(sqr(x1)))
   MARK(add(x0, sqr(terms(z0)))) -> c17(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0))))
   MARK(add(x0, sqr(sqr(z0)))) -> c17(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0))))
   MARK(add(x0, sqr(add(z0, z1)))) -> c17(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1))))
   MARK(add(x0, sqr(dbl(z0)))) -> c17(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0))))
   MARK(add(x0, sqr(first(z0, z1)))) -> c17(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1))))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1))))
   MARK(add(x0, sqr(recip(z0)))) -> c17(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0))))
   MARK(add(x0, sqr(s(z0)))) -> c17(A__ADD(mark(x0), a__sqr(s(z0))), MARK(sqr(s(z0))))
   MARK(add(x0, sqr(0))) -> c17(A__ADD(mark(x0), a__sqr(0)), MARK(sqr(0)))
   MARK(add(x0, sqr(nil))) -> c17(A__ADD(mark(x0), a__sqr(nil)), MARK(sqr(nil)))
   MARK(add(terms(z0), sqr(x1))) -> c17(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(sqr(x1)))
   MARK(add(sqr(z0), sqr(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(x1)))
   MARK(add(add(z0, z1), sqr(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(sqr(x1)))
   MARK(add(dbl(z0), sqr(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(sqr(x1)))
   MARK(add(first(z0, z1), sqr(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(sqr(x1)))
   MARK(add(0, sqr(x1))) -> c17(A__ADD(0, a__sqr(mark(x1))), MARK(sqr(x1)))
   MARK(add(x0, sqr(x1))) -> c17(MARK(sqr(x1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c17(MARK(sqr(x1)))
   MARK(add(recip(z0), sqr(x1))) -> c17(MARK(sqr(x1)))
   MARK(add(s(z0), sqr(x1))) -> c17(MARK(sqr(x1)))
   MARK(add(nil, sqr(x1))) -> c17(MARK(sqr(x1)))
   MARK(add(x0, add(x1, x2))) -> c17(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(add(x1, x2)))
   MARK(add(x0, add(x1, terms(z0)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(add(x1, terms(z0))))
   MARK(add(x0, add(x1, sqr(z0)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(add(x1, sqr(z0))))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(add(x1, add(z0, z1))))
   MARK(add(x0, add(x1, dbl(z0)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(add(x1, dbl(z0))))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(add(x1, first(z0, z1))))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(add(x1, cons(z0, z1))))
   MARK(add(x0, add(x1, recip(z0)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(add(x1, recip(z0))))
   MARK(add(x0, add(x1, s(z0)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(add(x1, s(z0))))
   MARK(add(x0, add(x1, 0))) -> c17(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(add(x1, 0)))
   MARK(add(x0, add(x1, nil))) -> c17(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(add(x1, nil)))
   MARK(add(x0, add(terms(z0), x2))) -> c17(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(add(terms(z0), x2)))
   MARK(add(x0, add(sqr(z0), x2))) -> c17(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(add(sqr(z0), x2)))
   MARK(add(x0, add(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(add(add(z0, z1), x2)))
   MARK(add(x0, add(dbl(z0), x2))) -> c17(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(add(dbl(z0), x2)))
   MARK(add(x0, add(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(add(first(z0, z1), x2)))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(add(cons(z0, z1), x2)))
   MARK(add(x0, add(recip(z0), x2))) -> c17(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(add(recip(z0), x2)))
   MARK(add(x0, add(s(z0), x2))) -> c17(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(add(s(z0), x2)))
   MARK(add(x0, add(0, x2))) -> c17(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(add(0, x2)))
   MARK(add(x0, add(nil, x2))) -> c17(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(add(nil, x2)))
   MARK(add(terms(z0), add(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2)))
   MARK(add(sqr(z0), add(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2)))
   MARK(add(add(z0, z1), add(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2)))
   MARK(add(dbl(z0), add(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2)))
   MARK(add(first(z0, z1), add(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2)))
   MARK(add(cons(z0, z1), add(x1, x2))) -> c17(A__ADD(cons(mark(z0), z1), a__add(mark(x1), mark(x2))), MARK(add(x1, x2)))
   MARK(add(recip(z0), add(x1, x2))) -> c17(A__ADD(recip(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2)))
   MARK(add(s(z0), add(x1, x2))) -> c17(A__ADD(s(z0), a__add(mark(x1), mark(x2))), MARK(add(x1, x2)))
   MARK(add(0, add(x1, x2))) -> c17(A__ADD(0, a__add(mark(x1), mark(x2))), MARK(add(x1, x2)))
   MARK(add(nil, add(x1, x2))) -> c17(A__ADD(nil, a__add(mark(x1), mark(x2))), MARK(add(x1, x2)))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
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   MARK(add(x0, add(x1, nil))) -> c17(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(add(x1, nil)))
   MARK(add(x0, add(terms(z0), x2))) -> c17(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(add(terms(z0), x2)))
   MARK(add(x0, add(sqr(z0), x2))) -> c17(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(add(sqr(z0), x2)))
   MARK(add(x0, add(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(add(add(z0, z1), x2)))
   MARK(add(x0, add(dbl(z0), x2))) -> c17(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(add(dbl(z0), x2)))
   MARK(add(x0, add(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(add(first(z0, z1), x2)))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(add(cons(z0, z1), x2)))
   MARK(add(x0, add(recip(z0), x2))) -> c17(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(add(recip(z0), x2)))
   MARK(add(x0, add(s(z0), x2))) -> c17(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(add(s(z0), x2)))
   MARK(add(x0, add(0, x2))) -> c17(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(add(0, x2)))
   MARK(add(x0, add(nil, x2))) -> c17(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(add(nil, x2)))
   MARK(add(terms(z0), add(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2)))
   MARK(add(sqr(z0), add(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2)))
   MARK(add(add(z0, z1), add(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2)))
   MARK(add(dbl(z0), add(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2)))
   MARK(add(first(z0, z1), add(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2)))
   MARK(add(cons(z0, z1), add(x1, x2))) -> c17(A__ADD(cons(mark(z0), z1), a__add(mark(x1), mark(x2))), MARK(add(x1, x2)))
   MARK(add(recip(z0), add(x1, x2))) -> c17(A__ADD(recip(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2)))
   MARK(add(s(z0), add(x1, x2))) -> c17(A__ADD(s(z0), a__add(mark(x1), mark(x2))), MARK(add(x1, x2)))
   MARK(add(0, add(x1, x2))) -> c17(A__ADD(0, a__add(mark(x1), mark(x2))), MARK(add(x1, x2)))
   MARK(add(nil, add(x1, x2))) -> c17(A__ADD(nil, a__add(mark(x1), mark(x2))), MARK(add(x1, x2)))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2


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

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

(142)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2))))
   MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0))
   MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0))
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   MARK(add(dbl(x0), x1)) -> c16(MARK(dbl(x0)))
   MARK(add(first(x0, terms(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(first(x0, terms(z0))))
   MARK(add(first(x0, sqr(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(first(x0, sqr(z0))))
   MARK(add(first(x0, add(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, add(z0, z1))))
   MARK(add(first(x0, dbl(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(first(x0, dbl(z0))))
   MARK(add(first(x0, first(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1))))
   MARK(add(first(x0, cons(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1))))
   MARK(add(first(x0, recip(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), recip(mark(z0))), mark(x2)), MARK(first(x0, recip(z0))))
   MARK(add(first(x0, s(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(first(x0, s(z0))))
   MARK(add(first(x0, 0), x2)) -> c16(A__ADD(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0)))
   MARK(add(first(x0, nil), x2)) -> c16(A__ADD(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil)))
   MARK(add(first(terms(z0), x1), x2)) -> c16(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(first(terms(z0), x1)))
   MARK(add(first(sqr(z0), x1), x2)) -> c16(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(first(sqr(z0), x1)))
   MARK(add(first(add(z0, z1), x1), x2)) -> c16(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(add(z0, z1), x1)))
   MARK(add(first(dbl(z0), x1), x2)) -> c16(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(first(dbl(z0), x1)))
   MARK(add(first(first(z0, z1), x1), x2)) -> c16(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1)))
   MARK(add(first(cons(z0, z1), x1), x2)) -> c16(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1)))
   MARK(add(first(recip(z0), x1), x2)) -> c16(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(first(recip(z0), x1)))
   MARK(add(first(s(z0), x1), x2)) -> c16(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(first(s(z0), x1)))
   MARK(add(first(0, x1), x2)) -> c16(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1)))
   MARK(add(first(nil, x1), x2)) -> c16(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1)))
   MARK(add(first(x0, x1), x2)) -> c16(MARK(first(x0, x1)))
   MARK(add(x0, terms(x1))) -> c17(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(terms(x1)))
   MARK(add(x0, terms(x1))) -> c17(A__ADD(mark(x0), terms(mark(x1))), MARK(terms(x1)))
   MARK(add(x0, terms(terms(z0)))) -> c17(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0))))
   MARK(add(x0, terms(sqr(z0)))) -> c17(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0))))
   MARK(add(x0, terms(add(z0, z1)))) -> c17(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1))))
   MARK(add(x0, terms(dbl(z0)))) -> c17(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0))))
   MARK(add(x0, terms(first(z0, z1)))) -> c17(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1))))
   MARK(add(x0, terms(cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1))))
   MARK(add(x0, terms(recip(z0)))) -> c17(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(terms(recip(z0))))
   MARK(add(x0, terms(s(z0)))) -> c17(A__ADD(mark(x0), a__terms(s(z0))), MARK(terms(s(z0))))
   MARK(add(x0, terms(0))) -> c17(A__ADD(mark(x0), a__terms(0)), MARK(terms(0)))
   MARK(add(x0, terms(nil))) -> c17(A__ADD(mark(x0), a__terms(nil)), MARK(terms(nil)))
   MARK(add(terms(z0), terms(x1))) -> c17(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(x1)))
   MARK(add(sqr(z0), terms(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(terms(x1)))
   MARK(add(add(z0, z1), terms(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(terms(x1)))
   MARK(add(dbl(z0), terms(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(terms(x1)))
   MARK(add(first(z0, z1), terms(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(terms(x1)))
   MARK(add(0, terms(x1))) -> c17(A__ADD(0, a__terms(mark(x1))), MARK(terms(x1)))
   MARK(add(x0, terms(x1))) -> c17(MARK(terms(x1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c17(MARK(terms(x1)))
   MARK(add(recip(z0), terms(x1))) -> c17(MARK(terms(x1)))
   MARK(add(s(z0), terms(x1))) -> c17(MARK(terms(x1)))
   MARK(add(nil, terms(x1))) -> c17(MARK(terms(x1)))
   MARK(add(x0, sqr(x1))) -> c17(A__ADD(mark(x0), sqr(mark(x1))), MARK(sqr(x1)))
   MARK(add(x0, sqr(terms(z0)))) -> c17(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0))))
   MARK(add(x0, sqr(sqr(z0)))) -> c17(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0))))
   MARK(add(x0, sqr(add(z0, z1)))) -> c17(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1))))
   MARK(add(x0, sqr(dbl(z0)))) -> c17(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0))))
   MARK(add(x0, sqr(first(z0, z1)))) -> c17(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1))))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1))))
   MARK(add(x0, sqr(recip(z0)))) -> c17(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0))))
   MARK(add(x0, sqr(s(z0)))) -> c17(A__ADD(mark(x0), a__sqr(s(z0))), MARK(sqr(s(z0))))
   MARK(add(x0, sqr(0))) -> c17(A__ADD(mark(x0), a__sqr(0)), MARK(sqr(0)))
   MARK(add(x0, sqr(nil))) -> c17(A__ADD(mark(x0), a__sqr(nil)), MARK(sqr(nil)))
   MARK(add(terms(z0), sqr(x1))) -> c17(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(sqr(x1)))
   MARK(add(sqr(z0), sqr(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(x1)))
   MARK(add(add(z0, z1), sqr(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(sqr(x1)))
   MARK(add(dbl(z0), sqr(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(sqr(x1)))
   MARK(add(first(z0, z1), sqr(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(sqr(x1)))
   MARK(add(0, sqr(x1))) -> c17(A__ADD(0, a__sqr(mark(x1))), MARK(sqr(x1)))
   MARK(add(x0, sqr(x1))) -> c17(MARK(sqr(x1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c17(MARK(sqr(x1)))
   MARK(add(recip(z0), sqr(x1))) -> c17(MARK(sqr(x1)))
   MARK(add(s(z0), sqr(x1))) -> c17(MARK(sqr(x1)))
   MARK(add(nil, sqr(x1))) -> c17(MARK(sqr(x1)))
   MARK(add(x0, add(x1, x2))) -> c17(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(add(x1, x2)))
   MARK(add(x0, add(x1, terms(z0)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(add(x1, terms(z0))))
   MARK(add(x0, add(x1, sqr(z0)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(add(x1, sqr(z0))))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(add(x1, add(z0, z1))))
   MARK(add(x0, add(x1, dbl(z0)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(add(x1, dbl(z0))))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(add(x1, first(z0, z1))))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(add(x1, cons(z0, z1))))
   MARK(add(x0, add(x1, recip(z0)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(add(x1, recip(z0))))
   MARK(add(x0, add(x1, s(z0)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(add(x1, s(z0))))
   MARK(add(x0, add(x1, 0))) -> c17(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(add(x1, 0)))
   MARK(add(x0, add(x1, nil))) -> c17(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(add(x1, nil)))
   MARK(add(x0, add(terms(z0), x2))) -> c17(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(add(terms(z0), x2)))
   MARK(add(x0, add(sqr(z0), x2))) -> c17(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(add(sqr(z0), x2)))
   MARK(add(x0, add(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(add(add(z0, z1), x2)))
   MARK(add(x0, add(dbl(z0), x2))) -> c17(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(add(dbl(z0), x2)))
   MARK(add(x0, add(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(add(first(z0, z1), x2)))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(add(cons(z0, z1), x2)))
   MARK(add(x0, add(recip(z0), x2))) -> c17(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(add(recip(z0), x2)))
   MARK(add(x0, add(s(z0), x2))) -> c17(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(add(s(z0), x2)))
   MARK(add(x0, add(0, x2))) -> c17(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(add(0, x2)))
   MARK(add(x0, add(nil, x2))) -> c17(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(add(nil, x2)))
   MARK(add(terms(z0), add(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2)))
   MARK(add(sqr(z0), add(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2)))
   MARK(add(add(z0, z1), add(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2)))
   MARK(add(dbl(z0), add(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2)))
   MARK(add(first(z0, z1), add(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2)))
   MARK(add(0, add(x1, x2))) -> c17(A__ADD(0, a__add(mark(x1), mark(x2))), MARK(add(x1, x2)))
   MARK(add(cons(z0, z1), add(x1, x2))) -> c17(MARK(add(x1, x2)))
   MARK(add(recip(z0), add(x1, x2))) -> c17(MARK(add(x1, x2)))
   MARK(add(s(z0), add(x1, x2))) -> c17(MARK(add(x1, x2)))
   MARK(add(nil, add(x1, x2))) -> c17(MARK(add(x1, x2)))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
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   MARK(add(x0, add(nil, x2))) -> c17(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(add(nil, x2)))
   MARK(add(terms(z0), add(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2)))
   MARK(add(sqr(z0), add(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2)))
   MARK(add(add(z0, z1), add(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2)))
   MARK(add(dbl(z0), add(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2)))
   MARK(add(first(z0, z1), add(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2)))
   MARK(add(0, add(x1, x2))) -> c17(A__ADD(0, a__add(mark(x1), mark(x2))), MARK(add(x1, x2)))
   MARK(add(cons(z0, z1), add(x1, x2))) -> c17(MARK(add(x1, x2)))
   MARK(add(recip(z0), add(x1, x2))) -> c17(MARK(add(x1, x2)))
   MARK(add(s(z0), add(x1, x2))) -> c17(MARK(add(x1, x2)))
   MARK(add(nil, add(x1, x2))) -> c17(MARK(add(x1, x2)))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2


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

(143) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) by 
   MARK(add(x0, dbl(x1))) -> c17(A__ADD(mark(x0), dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(x0, dbl(terms(z0)))) -> c17(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0))))
   MARK(add(x0, dbl(sqr(z0)))) -> c17(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0))))
   MARK(add(x0, dbl(add(z0, z1)))) -> c17(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1))))
   MARK(add(x0, dbl(dbl(z0)))) -> c17(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0))))
   MARK(add(x0, dbl(first(z0, z1)))) -> c17(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1))))
   MARK(add(x0, dbl(cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1))))
   MARK(add(x0, dbl(recip(z0)))) -> c17(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0))))
   MARK(add(x0, dbl(s(z0)))) -> c17(A__ADD(mark(x0), a__dbl(s(z0))), MARK(dbl(s(z0))))
   MARK(add(x0, dbl(0))) -> c17(A__ADD(mark(x0), a__dbl(0)), MARK(dbl(0)))
   MARK(add(x0, dbl(nil))) -> c17(A__ADD(mark(x0), a__dbl(nil)), MARK(dbl(nil)))
   MARK(add(terms(z0), dbl(x1))) -> c17(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(sqr(z0), dbl(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(add(z0, z1), dbl(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(dbl(z0), dbl(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(first(z0, z1), dbl(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(cons(z0, z1), dbl(x1))) -> c17(A__ADD(cons(mark(z0), z1), a__dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(recip(z0), dbl(x1))) -> c17(A__ADD(recip(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(s(z0), dbl(x1))) -> c17(A__ADD(s(z0), a__dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(0, dbl(x1))) -> c17(A__ADD(0, a__dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(nil, dbl(x1))) -> c17(A__ADD(nil, a__dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(x0, dbl(x1))) -> c17(MARK(dbl(x1)))

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

(144)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
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   MARK(add(dbl(sqr(z0)), x1)) -> c16(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(dbl(sqr(z0))))
   MARK(add(dbl(add(z0, z1)), x1)) -> c16(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(dbl(add(z0, z1))))
   MARK(add(dbl(dbl(z0)), x1)) -> c16(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(dbl(dbl(z0))))
   MARK(add(dbl(first(z0, z1)), x1)) -> c16(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(dbl(first(z0, z1))))
   MARK(add(dbl(cons(z0, z1)), x1)) -> c16(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(dbl(cons(z0, z1))))
   MARK(add(dbl(recip(z0)), x1)) -> c16(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(dbl(recip(z0))))
   MARK(add(dbl(s(z0)), x1)) -> c16(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(dbl(s(z0))))
   MARK(add(dbl(0), x1)) -> c16(A__ADD(a__dbl(0), mark(x1)), MARK(dbl(0)))
   MARK(add(dbl(nil), x1)) -> c16(A__ADD(a__dbl(nil), mark(x1)), MARK(dbl(nil)))
   MARK(add(dbl(x0), x1)) -> c16(MARK(dbl(x0)))
   MARK(add(first(x0, terms(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(first(x0, terms(z0))))
   MARK(add(first(x0, sqr(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(first(x0, sqr(z0))))
   MARK(add(first(x0, add(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, add(z0, z1))))
   MARK(add(first(x0, dbl(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(first(x0, dbl(z0))))
   MARK(add(first(x0, first(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1))))
   MARK(add(first(x0, cons(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1))))
   MARK(add(first(x0, recip(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), recip(mark(z0))), mark(x2)), MARK(first(x0, recip(z0))))
   MARK(add(first(x0, s(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(first(x0, s(z0))))
   MARK(add(first(x0, 0), x2)) -> c16(A__ADD(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0)))
   MARK(add(first(x0, nil), x2)) -> c16(A__ADD(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil)))
   MARK(add(first(terms(z0), x1), x2)) -> c16(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(first(terms(z0), x1)))
   MARK(add(first(sqr(z0), x1), x2)) -> c16(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(first(sqr(z0), x1)))
   MARK(add(first(add(z0, z1), x1), x2)) -> c16(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(add(z0, z1), x1)))
   MARK(add(first(dbl(z0), x1), x2)) -> c16(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(first(dbl(z0), x1)))
   MARK(add(first(first(z0, z1), x1), x2)) -> c16(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1)))
   MARK(add(first(cons(z0, z1), x1), x2)) -> c16(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1)))
   MARK(add(first(recip(z0), x1), x2)) -> c16(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(first(recip(z0), x1)))
   MARK(add(first(s(z0), x1), x2)) -> c16(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(first(s(z0), x1)))
   MARK(add(first(0, x1), x2)) -> c16(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1)))
   MARK(add(first(nil, x1), x2)) -> c16(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1)))
   MARK(add(first(x0, x1), x2)) -> c16(MARK(first(x0, x1)))
   MARK(add(x0, terms(x1))) -> c17(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(terms(x1)))
   MARK(add(x0, terms(x1))) -> c17(A__ADD(mark(x0), terms(mark(x1))), MARK(terms(x1)))
   MARK(add(x0, terms(terms(z0)))) -> c17(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0))))
   MARK(add(x0, terms(sqr(z0)))) -> c17(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0))))
   MARK(add(x0, terms(add(z0, z1)))) -> c17(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1))))
   MARK(add(x0, terms(dbl(z0)))) -> c17(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0))))
   MARK(add(x0, terms(first(z0, z1)))) -> c17(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1))))
   MARK(add(x0, terms(cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1))))
   MARK(add(x0, terms(recip(z0)))) -> c17(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(terms(recip(z0))))
   MARK(add(x0, terms(s(z0)))) -> c17(A__ADD(mark(x0), a__terms(s(z0))), MARK(terms(s(z0))))
   MARK(add(x0, terms(0))) -> c17(A__ADD(mark(x0), a__terms(0)), MARK(terms(0)))
   MARK(add(x0, terms(nil))) -> c17(A__ADD(mark(x0), a__terms(nil)), MARK(terms(nil)))
   MARK(add(terms(z0), terms(x1))) -> c17(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(x1)))
   MARK(add(sqr(z0), terms(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(terms(x1)))
   MARK(add(add(z0, z1), terms(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(terms(x1)))
   MARK(add(dbl(z0), terms(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(terms(x1)))
   MARK(add(first(z0, z1), terms(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(terms(x1)))
   MARK(add(0, terms(x1))) -> c17(A__ADD(0, a__terms(mark(x1))), MARK(terms(x1)))
   MARK(add(x0, terms(x1))) -> c17(MARK(terms(x1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c17(MARK(terms(x1)))
   MARK(add(recip(z0), terms(x1))) -> c17(MARK(terms(x1)))
   MARK(add(s(z0), terms(x1))) -> c17(MARK(terms(x1)))
   MARK(add(nil, terms(x1))) -> c17(MARK(terms(x1)))
   MARK(add(x0, sqr(x1))) -> c17(A__ADD(mark(x0), sqr(mark(x1))), MARK(sqr(x1)))
   MARK(add(x0, sqr(terms(z0)))) -> c17(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0))))
   MARK(add(x0, sqr(sqr(z0)))) -> c17(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0))))
   MARK(add(x0, sqr(add(z0, z1)))) -> c17(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1))))
   MARK(add(x0, sqr(dbl(z0)))) -> c17(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0))))
   MARK(add(x0, sqr(first(z0, z1)))) -> c17(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1))))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1))))
   MARK(add(x0, sqr(recip(z0)))) -> c17(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0))))
   MARK(add(x0, sqr(s(z0)))) -> c17(A__ADD(mark(x0), a__sqr(s(z0))), MARK(sqr(s(z0))))
   MARK(add(x0, sqr(0))) -> c17(A__ADD(mark(x0), a__sqr(0)), MARK(sqr(0)))
   MARK(add(x0, sqr(nil))) -> c17(A__ADD(mark(x0), a__sqr(nil)), MARK(sqr(nil)))
   MARK(add(terms(z0), sqr(x1))) -> c17(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(sqr(x1)))
   MARK(add(sqr(z0), sqr(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(x1)))
   MARK(add(add(z0, z1), sqr(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(sqr(x1)))
   MARK(add(dbl(z0), sqr(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(sqr(x1)))
   MARK(add(first(z0, z1), sqr(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(sqr(x1)))
   MARK(add(0, sqr(x1))) -> c17(A__ADD(0, a__sqr(mark(x1))), MARK(sqr(x1)))
   MARK(add(x0, sqr(x1))) -> c17(MARK(sqr(x1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c17(MARK(sqr(x1)))
   MARK(add(recip(z0), sqr(x1))) -> c17(MARK(sqr(x1)))
   MARK(add(s(z0), sqr(x1))) -> c17(MARK(sqr(x1)))
   MARK(add(nil, sqr(x1))) -> c17(MARK(sqr(x1)))
   MARK(add(x0, add(x1, x2))) -> c17(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(add(x1, x2)))
   MARK(add(x0, add(x1, terms(z0)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(add(x1, terms(z0))))
   MARK(add(x0, add(x1, sqr(z0)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(add(x1, sqr(z0))))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(add(x1, add(z0, z1))))
   MARK(add(x0, add(x1, dbl(z0)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(add(x1, dbl(z0))))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(add(x1, first(z0, z1))))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(add(x1, cons(z0, z1))))
   MARK(add(x0, add(x1, recip(z0)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(add(x1, recip(z0))))
   MARK(add(x0, add(x1, s(z0)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(add(x1, s(z0))))
   MARK(add(x0, add(x1, 0))) -> c17(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(add(x1, 0)))
   MARK(add(x0, add(x1, nil))) -> c17(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(add(x1, nil)))
   MARK(add(x0, add(terms(z0), x2))) -> c17(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(add(terms(z0), x2)))
   MARK(add(x0, add(sqr(z0), x2))) -> c17(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(add(sqr(z0), x2)))
   MARK(add(x0, add(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(add(add(z0, z1), x2)))
   MARK(add(x0, add(dbl(z0), x2))) -> c17(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(add(dbl(z0), x2)))
   MARK(add(x0, add(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(add(first(z0, z1), x2)))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(add(cons(z0, z1), x2)))
   MARK(add(x0, add(recip(z0), x2))) -> c17(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(add(recip(z0), x2)))
   MARK(add(x0, add(s(z0), x2))) -> c17(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(add(s(z0), x2)))
   MARK(add(x0, add(0, x2))) -> c17(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(add(0, x2)))
   MARK(add(x0, add(nil, x2))) -> c17(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(add(nil, x2)))
   MARK(add(terms(z0), add(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2)))
   MARK(add(sqr(z0), add(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2)))
   MARK(add(add(z0, z1), add(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2)))
   MARK(add(dbl(z0), add(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2)))
   MARK(add(first(z0, z1), add(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2)))
   MARK(add(0, add(x1, x2))) -> c17(A__ADD(0, a__add(mark(x1), mark(x2))), MARK(add(x1, x2)))
   MARK(add(cons(z0, z1), add(x1, x2))) -> c17(MARK(add(x1, x2)))
   MARK(add(recip(z0), add(x1, x2))) -> c17(MARK(add(x1, x2)))
   MARK(add(s(z0), add(x1, x2))) -> c17(MARK(add(x1, x2)))
   MARK(add(nil, add(x1, x2))) -> c17(MARK(add(x1, x2)))
   MARK(add(x0, dbl(x1))) -> c17(A__ADD(mark(x0), dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(x0, dbl(terms(z0)))) -> c17(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0))))
   MARK(add(x0, dbl(sqr(z0)))) -> c17(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0))))
   MARK(add(x0, dbl(add(z0, z1)))) -> c17(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1))))
   MARK(add(x0, dbl(dbl(z0)))) -> c17(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0))))
   MARK(add(x0, dbl(first(z0, z1)))) -> c17(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1))))
   MARK(add(x0, dbl(cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1))))
   MARK(add(x0, dbl(recip(z0)))) -> c17(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0))))
   MARK(add(x0, dbl(s(z0)))) -> c17(A__ADD(mark(x0), a__dbl(s(z0))), MARK(dbl(s(z0))))
   MARK(add(x0, dbl(0))) -> c17(A__ADD(mark(x0), a__dbl(0)), MARK(dbl(0)))
   MARK(add(x0, dbl(nil))) -> c17(A__ADD(mark(x0), a__dbl(nil)), MARK(dbl(nil)))
   MARK(add(terms(z0), dbl(x1))) -> c17(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(sqr(z0), dbl(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(add(z0, z1), dbl(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(dbl(z0), dbl(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(first(z0, z1), dbl(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(cons(z0, z1), dbl(x1))) -> c17(A__ADD(cons(mark(z0), z1), a__dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(recip(z0), dbl(x1))) -> c17(A__ADD(recip(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(s(z0), dbl(x1))) -> c17(A__ADD(s(z0), a__dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(0, dbl(x1))) -> c17(A__ADD(0, a__dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(nil, dbl(x1))) -> c17(A__ADD(nil, a__dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(x0, dbl(x1))) -> c17(MARK(dbl(x1)))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
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   MARK(add(sqr(z0), sqr(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(x1)))
   MARK(add(add(z0, z1), sqr(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(sqr(x1)))
   MARK(add(dbl(z0), sqr(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(sqr(x1)))
   MARK(add(first(z0, z1), sqr(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(sqr(x1)))
   MARK(add(0, sqr(x1))) -> c17(A__ADD(0, a__sqr(mark(x1))), MARK(sqr(x1)))
   MARK(add(x0, sqr(x1))) -> c17(MARK(sqr(x1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c17(MARK(sqr(x1)))
   MARK(add(recip(z0), sqr(x1))) -> c17(MARK(sqr(x1)))
   MARK(add(s(z0), sqr(x1))) -> c17(MARK(sqr(x1)))
   MARK(add(nil, sqr(x1))) -> c17(MARK(sqr(x1)))
   MARK(add(x0, add(x1, x2))) -> c17(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(add(x1, x2)))
   MARK(add(x0, add(x1, terms(z0)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(add(x1, terms(z0))))
   MARK(add(x0, add(x1, sqr(z0)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(add(x1, sqr(z0))))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(add(x1, add(z0, z1))))
   MARK(add(x0, add(x1, dbl(z0)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(add(x1, dbl(z0))))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(add(x1, first(z0, z1))))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(add(x1, cons(z0, z1))))
   MARK(add(x0, add(x1, recip(z0)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(add(x1, recip(z0))))
   MARK(add(x0, add(x1, s(z0)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(add(x1, s(z0))))
   MARK(add(x0, add(x1, 0))) -> c17(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(add(x1, 0)))
   MARK(add(x0, add(x1, nil))) -> c17(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(add(x1, nil)))
   MARK(add(x0, add(terms(z0), x2))) -> c17(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(add(terms(z0), x2)))
   MARK(add(x0, add(sqr(z0), x2))) -> c17(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(add(sqr(z0), x2)))
   MARK(add(x0, add(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(add(add(z0, z1), x2)))
   MARK(add(x0, add(dbl(z0), x2))) -> c17(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(add(dbl(z0), x2)))
   MARK(add(x0, add(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(add(first(z0, z1), x2)))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(add(cons(z0, z1), x2)))
   MARK(add(x0, add(recip(z0), x2))) -> c17(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(add(recip(z0), x2)))
   MARK(add(x0, add(s(z0), x2))) -> c17(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(add(s(z0), x2)))
   MARK(add(x0, add(0, x2))) -> c17(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(add(0, x2)))
   MARK(add(x0, add(nil, x2))) -> c17(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(add(nil, x2)))
   MARK(add(terms(z0), add(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2)))
   MARK(add(sqr(z0), add(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2)))
   MARK(add(add(z0, z1), add(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2)))
   MARK(add(dbl(z0), add(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2)))
   MARK(add(first(z0, z1), add(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2)))
   MARK(add(0, add(x1, x2))) -> c17(A__ADD(0, a__add(mark(x1), mark(x2))), MARK(add(x1, x2)))
   MARK(add(cons(z0, z1), add(x1, x2))) -> c17(MARK(add(x1, x2)))
   MARK(add(recip(z0), add(x1, x2))) -> c17(MARK(add(x1, x2)))
   MARK(add(s(z0), add(x1, x2))) -> c17(MARK(add(x1, x2)))
   MARK(add(nil, add(x1, x2))) -> c17(MARK(add(x1, x2)))
   MARK(add(x0, dbl(x1))) -> c17(A__ADD(mark(x0), dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(x0, dbl(terms(z0)))) -> c17(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0))))
   MARK(add(x0, dbl(sqr(z0)))) -> c17(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0))))
   MARK(add(x0, dbl(add(z0, z1)))) -> c17(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1))))
   MARK(add(x0, dbl(dbl(z0)))) -> c17(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0))))
   MARK(add(x0, dbl(first(z0, z1)))) -> c17(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1))))
   MARK(add(x0, dbl(cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1))))
   MARK(add(x0, dbl(recip(z0)))) -> c17(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0))))
   MARK(add(x0, dbl(s(z0)))) -> c17(A__ADD(mark(x0), a__dbl(s(z0))), MARK(dbl(s(z0))))
   MARK(add(x0, dbl(0))) -> c17(A__ADD(mark(x0), a__dbl(0)), MARK(dbl(0)))
   MARK(add(x0, dbl(nil))) -> c17(A__ADD(mark(x0), a__dbl(nil)), MARK(dbl(nil)))
   MARK(add(terms(z0), dbl(x1))) -> c17(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(sqr(z0), dbl(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(add(z0, z1), dbl(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(dbl(z0), dbl(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(first(z0, z1), dbl(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(cons(z0, z1), dbl(x1))) -> c17(A__ADD(cons(mark(z0), z1), a__dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(recip(z0), dbl(x1))) -> c17(A__ADD(recip(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(s(z0), dbl(x1))) -> c17(A__ADD(s(z0), a__dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(0, dbl(x1))) -> c17(A__ADD(0, a__dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(nil, dbl(x1))) -> c17(A__ADD(nil, a__dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(x0, dbl(x1))) -> c17(MARK(dbl(x1)))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2


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

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

(146)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
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   MARK(add(x0, dbl(0))) -> c17(A__ADD(mark(x0), a__dbl(0)), MARK(dbl(0)))
   MARK(add(x0, dbl(nil))) -> c17(A__ADD(mark(x0), a__dbl(nil)), MARK(dbl(nil)))
   MARK(add(terms(z0), dbl(x1))) -> c17(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(sqr(z0), dbl(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(add(z0, z1), dbl(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(dbl(z0), dbl(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(first(z0, z1), dbl(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(0, dbl(x1))) -> c17(A__ADD(0, a__dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(x0, dbl(x1))) -> c17(MARK(dbl(x1)))
   MARK(add(cons(z0, z1), dbl(x1))) -> c17(MARK(dbl(x1)))
   MARK(add(recip(z0), dbl(x1))) -> c17(MARK(dbl(x1)))
   MARK(add(s(z0), dbl(x1))) -> c17(MARK(dbl(x1)))
   MARK(add(nil, dbl(x1))) -> c17(MARK(dbl(x1)))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2))))
   MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0))
   MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0))
   MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0))
   MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0))
   MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1))))
   MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0))
   MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0))
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   MARK(add(x0, terms(terms(z0)))) -> c17(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0))))
   MARK(add(x0, terms(sqr(z0)))) -> c17(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0))))
   MARK(add(x0, terms(add(z0, z1)))) -> c17(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1))))
   MARK(add(x0, terms(dbl(z0)))) -> c17(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0))))
   MARK(add(x0, terms(first(z0, z1)))) -> c17(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1))))
   MARK(add(x0, terms(cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1))))
   MARK(add(x0, terms(recip(z0)))) -> c17(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(terms(recip(z0))))
   MARK(add(x0, terms(s(z0)))) -> c17(A__ADD(mark(x0), a__terms(s(z0))), MARK(terms(s(z0))))
   MARK(add(x0, terms(0))) -> c17(A__ADD(mark(x0), a__terms(0)), MARK(terms(0)))
   MARK(add(x0, terms(nil))) -> c17(A__ADD(mark(x0), a__terms(nil)), MARK(terms(nil)))
   MARK(add(terms(z0), terms(x1))) -> c17(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(x1)))
   MARK(add(sqr(z0), terms(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(terms(x1)))
   MARK(add(add(z0, z1), terms(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(terms(x1)))
   MARK(add(dbl(z0), terms(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(terms(x1)))
   MARK(add(first(z0, z1), terms(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(terms(x1)))
   MARK(add(0, terms(x1))) -> c17(A__ADD(0, a__terms(mark(x1))), MARK(terms(x1)))
   MARK(add(x0, terms(x1))) -> c17(MARK(terms(x1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c17(MARK(terms(x1)))
   MARK(add(recip(z0), terms(x1))) -> c17(MARK(terms(x1)))
   MARK(add(s(z0), terms(x1))) -> c17(MARK(terms(x1)))
   MARK(add(nil, terms(x1))) -> c17(MARK(terms(x1)))
   MARK(add(x0, sqr(x1))) -> c17(A__ADD(mark(x0), sqr(mark(x1))), MARK(sqr(x1)))
   MARK(add(x0, sqr(terms(z0)))) -> c17(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0))))
   MARK(add(x0, sqr(sqr(z0)))) -> c17(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0))))
   MARK(add(x0, sqr(add(z0, z1)))) -> c17(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1))))
   MARK(add(x0, sqr(dbl(z0)))) -> c17(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0))))
   MARK(add(x0, sqr(first(z0, z1)))) -> c17(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1))))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1))))
   MARK(add(x0, sqr(recip(z0)))) -> c17(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0))))
   MARK(add(x0, sqr(s(z0)))) -> c17(A__ADD(mark(x0), a__sqr(s(z0))), MARK(sqr(s(z0))))
   MARK(add(x0, sqr(0))) -> c17(A__ADD(mark(x0), a__sqr(0)), MARK(sqr(0)))
   MARK(add(x0, sqr(nil))) -> c17(A__ADD(mark(x0), a__sqr(nil)), MARK(sqr(nil)))
   MARK(add(terms(z0), sqr(x1))) -> c17(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(sqr(x1)))
   MARK(add(sqr(z0), sqr(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(x1)))
   MARK(add(add(z0, z1), sqr(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(sqr(x1)))
   MARK(add(dbl(z0), sqr(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(sqr(x1)))
   MARK(add(first(z0, z1), sqr(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(sqr(x1)))
   MARK(add(0, sqr(x1))) -> c17(A__ADD(0, a__sqr(mark(x1))), MARK(sqr(x1)))
   MARK(add(x0, sqr(x1))) -> c17(MARK(sqr(x1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c17(MARK(sqr(x1)))
   MARK(add(recip(z0), sqr(x1))) -> c17(MARK(sqr(x1)))
   MARK(add(s(z0), sqr(x1))) -> c17(MARK(sqr(x1)))
   MARK(add(nil, sqr(x1))) -> c17(MARK(sqr(x1)))
   MARK(add(x0, add(x1, x2))) -> c17(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(add(x1, x2)))
   MARK(add(x0, add(x1, terms(z0)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(add(x1, terms(z0))))
   MARK(add(x0, add(x1, sqr(z0)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(add(x1, sqr(z0))))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(add(x1, add(z0, z1))))
   MARK(add(x0, add(x1, dbl(z0)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(add(x1, dbl(z0))))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(add(x1, first(z0, z1))))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(add(x1, cons(z0, z1))))
   MARK(add(x0, add(x1, recip(z0)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(add(x1, recip(z0))))
   MARK(add(x0, add(x1, s(z0)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(add(x1, s(z0))))
   MARK(add(x0, add(x1, 0))) -> c17(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(add(x1, 0)))
   MARK(add(x0, add(x1, nil))) -> c17(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(add(x1, nil)))
   MARK(add(x0, add(terms(z0), x2))) -> c17(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(add(terms(z0), x2)))
   MARK(add(x0, add(sqr(z0), x2))) -> c17(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(add(sqr(z0), x2)))
   MARK(add(x0, add(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(add(add(z0, z1), x2)))
   MARK(add(x0, add(dbl(z0), x2))) -> c17(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(add(dbl(z0), x2)))
   MARK(add(x0, add(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(add(first(z0, z1), x2)))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(add(cons(z0, z1), x2)))
   MARK(add(x0, add(recip(z0), x2))) -> c17(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(add(recip(z0), x2)))
   MARK(add(x0, add(s(z0), x2))) -> c17(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(add(s(z0), x2)))
   MARK(add(x0, add(0, x2))) -> c17(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(add(0, x2)))
   MARK(add(x0, add(nil, x2))) -> c17(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(add(nil, x2)))
   MARK(add(terms(z0), add(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2)))
   MARK(add(sqr(z0), add(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2)))
   MARK(add(add(z0, z1), add(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2)))
   MARK(add(dbl(z0), add(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2)))
   MARK(add(first(z0, z1), add(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2)))
   MARK(add(0, add(x1, x2))) -> c17(A__ADD(0, a__add(mark(x1), mark(x2))), MARK(add(x1, x2)))
   MARK(add(cons(z0, z1), add(x1, x2))) -> c17(MARK(add(x1, x2)))
   MARK(add(recip(z0), add(x1, x2))) -> c17(MARK(add(x1, x2)))
   MARK(add(s(z0), add(x1, x2))) -> c17(MARK(add(x1, x2)))
   MARK(add(nil, add(x1, x2))) -> c17(MARK(add(x1, x2)))
   MARK(add(x0, dbl(x1))) -> c17(A__ADD(mark(x0), dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(x0, dbl(terms(z0)))) -> c17(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0))))
   MARK(add(x0, dbl(sqr(z0)))) -> c17(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0))))
   MARK(add(x0, dbl(add(z0, z1)))) -> c17(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1))))
   MARK(add(x0, dbl(dbl(z0)))) -> c17(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0))))
   MARK(add(x0, dbl(first(z0, z1)))) -> c17(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1))))
   MARK(add(x0, dbl(cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1))))
   MARK(add(x0, dbl(recip(z0)))) -> c17(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0))))
   MARK(add(x0, dbl(s(z0)))) -> c17(A__ADD(mark(x0), a__dbl(s(z0))), MARK(dbl(s(z0))))
   MARK(add(x0, dbl(0))) -> c17(A__ADD(mark(x0), a__dbl(0)), MARK(dbl(0)))
   MARK(add(x0, dbl(nil))) -> c17(A__ADD(mark(x0), a__dbl(nil)), MARK(dbl(nil)))
   MARK(add(terms(z0), dbl(x1))) -> c17(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(sqr(z0), dbl(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(add(z0, z1), dbl(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(dbl(z0), dbl(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(first(z0, z1), dbl(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(0, dbl(x1))) -> c17(A__ADD(0, a__dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(x0, dbl(x1))) -> c17(MARK(dbl(x1)))
   MARK(add(cons(z0, z1), dbl(x1))) -> c17(MARK(dbl(x1)))
   MARK(add(recip(z0), dbl(x1))) -> c17(MARK(dbl(x1)))
   MARK(add(s(z0), dbl(x1))) -> c17(MARK(dbl(x1)))
   MARK(add(nil, dbl(x1))) -> c17(MARK(dbl(x1)))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2


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

(147) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) by 
   MARK(add(x0, first(x1, x2))) -> c17(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(x0, first(x1, terms(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(first(x1, terms(z0))))
   MARK(add(x0, first(x1, sqr(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(first(x1, sqr(z0))))
   MARK(add(x0, first(x1, add(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(first(x1, add(z0, z1))))
   MARK(add(x0, first(x1, dbl(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(first(x1, dbl(z0))))
   MARK(add(x0, first(x1, first(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1))))
   MARK(add(x0, first(x1, cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1))))
   MARK(add(x0, first(x1, recip(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(first(x1, recip(z0))))
   MARK(add(x0, first(x1, s(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(first(x1, s(z0))))
   MARK(add(x0, first(x1, 0))) -> c17(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0)))
   MARK(add(x0, first(x1, nil))) -> c17(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil)))
   MARK(add(x0, first(terms(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(first(terms(z0), x2)))
   MARK(add(x0, first(sqr(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(first(sqr(z0), x2)))
   MARK(add(x0, first(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(first(add(z0, z1), x2)))
   MARK(add(x0, first(dbl(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(first(dbl(z0), x2)))
   MARK(add(x0, first(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2)))
   MARK(add(x0, first(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2)))
   MARK(add(x0, first(recip(z0), x2))) -> c17(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(first(recip(z0), x2)))
   MARK(add(x0, first(s(z0), x2))) -> c17(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(first(s(z0), x2)))
   MARK(add(x0, first(0, x2))) -> c17(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2)))
   MARK(add(x0, first(nil, x2))) -> c17(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2)))
   MARK(add(terms(z0), first(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(sqr(z0), first(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(add(z0, z1), first(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(dbl(z0), first(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(first(z0, z1), first(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(cons(z0, z1), first(x1, x2))) -> c17(A__ADD(cons(mark(z0), z1), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(recip(z0), first(x1, x2))) -> c17(A__ADD(recip(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(s(z0), first(x1, x2))) -> c17(A__ADD(s(z0), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(0, first(x1, x2))) -> c17(A__ADD(0, a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(nil, first(x1, x2))) -> c17(A__ADD(nil, a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))

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

(148)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
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   MARK(add(x0, sqr(terms(z0)))) -> c17(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0))))
   MARK(add(x0, sqr(sqr(z0)))) -> c17(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0))))
   MARK(add(x0, sqr(add(z0, z1)))) -> c17(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1))))
   MARK(add(x0, sqr(dbl(z0)))) -> c17(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0))))
   MARK(add(x0, sqr(first(z0, z1)))) -> c17(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1))))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1))))
   MARK(add(x0, sqr(recip(z0)))) -> c17(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0))))
   MARK(add(x0, sqr(s(z0)))) -> c17(A__ADD(mark(x0), a__sqr(s(z0))), MARK(sqr(s(z0))))
   MARK(add(x0, sqr(0))) -> c17(A__ADD(mark(x0), a__sqr(0)), MARK(sqr(0)))
   MARK(add(x0, sqr(nil))) -> c17(A__ADD(mark(x0), a__sqr(nil)), MARK(sqr(nil)))
   MARK(add(terms(z0), sqr(x1))) -> c17(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(sqr(x1)))
   MARK(add(sqr(z0), sqr(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(x1)))
   MARK(add(add(z0, z1), sqr(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(sqr(x1)))
   MARK(add(dbl(z0), sqr(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(sqr(x1)))
   MARK(add(first(z0, z1), sqr(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(sqr(x1)))
   MARK(add(0, sqr(x1))) -> c17(A__ADD(0, a__sqr(mark(x1))), MARK(sqr(x1)))
   MARK(add(x0, sqr(x1))) -> c17(MARK(sqr(x1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c17(MARK(sqr(x1)))
   MARK(add(recip(z0), sqr(x1))) -> c17(MARK(sqr(x1)))
   MARK(add(s(z0), sqr(x1))) -> c17(MARK(sqr(x1)))
   MARK(add(nil, sqr(x1))) -> c17(MARK(sqr(x1)))
   MARK(add(x0, add(x1, x2))) -> c17(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(add(x1, x2)))
   MARK(add(x0, add(x1, terms(z0)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(add(x1, terms(z0))))
   MARK(add(x0, add(x1, sqr(z0)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(add(x1, sqr(z0))))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(add(x1, add(z0, z1))))
   MARK(add(x0, add(x1, dbl(z0)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(add(x1, dbl(z0))))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(add(x1, first(z0, z1))))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(add(x1, cons(z0, z1))))
   MARK(add(x0, add(x1, recip(z0)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(add(x1, recip(z0))))
   MARK(add(x0, add(x1, s(z0)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(add(x1, s(z0))))
   MARK(add(x0, add(x1, 0))) -> c17(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(add(x1, 0)))
   MARK(add(x0, add(x1, nil))) -> c17(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(add(x1, nil)))
   MARK(add(x0, add(terms(z0), x2))) -> c17(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(add(terms(z0), x2)))
   MARK(add(x0, add(sqr(z0), x2))) -> c17(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(add(sqr(z0), x2)))
   MARK(add(x0, add(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(add(add(z0, z1), x2)))
   MARK(add(x0, add(dbl(z0), x2))) -> c17(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(add(dbl(z0), x2)))
   MARK(add(x0, add(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(add(first(z0, z1), x2)))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(add(cons(z0, z1), x2)))
   MARK(add(x0, add(recip(z0), x2))) -> c17(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(add(recip(z0), x2)))
   MARK(add(x0, add(s(z0), x2))) -> c17(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(add(s(z0), x2)))
   MARK(add(x0, add(0, x2))) -> c17(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(add(0, x2)))
   MARK(add(x0, add(nil, x2))) -> c17(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(add(nil, x2)))
   MARK(add(terms(z0), add(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2)))
   MARK(add(sqr(z0), add(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2)))
   MARK(add(add(z0, z1), add(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2)))
   MARK(add(dbl(z0), add(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2)))
   MARK(add(first(z0, z1), add(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2)))
   MARK(add(0, add(x1, x2))) -> c17(A__ADD(0, a__add(mark(x1), mark(x2))), MARK(add(x1, x2)))
   MARK(add(cons(z0, z1), add(x1, x2))) -> c17(MARK(add(x1, x2)))
   MARK(add(recip(z0), add(x1, x2))) -> c17(MARK(add(x1, x2)))
   MARK(add(s(z0), add(x1, x2))) -> c17(MARK(add(x1, x2)))
   MARK(add(nil, add(x1, x2))) -> c17(MARK(add(x1, x2)))
   MARK(add(x0, dbl(x1))) -> c17(A__ADD(mark(x0), dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(x0, dbl(terms(z0)))) -> c17(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0))))
   MARK(add(x0, dbl(sqr(z0)))) -> c17(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0))))
   MARK(add(x0, dbl(add(z0, z1)))) -> c17(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1))))
   MARK(add(x0, dbl(dbl(z0)))) -> c17(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0))))
   MARK(add(x0, dbl(first(z0, z1)))) -> c17(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1))))
   MARK(add(x0, dbl(cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1))))
   MARK(add(x0, dbl(recip(z0)))) -> c17(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0))))
   MARK(add(x0, dbl(s(z0)))) -> c17(A__ADD(mark(x0), a__dbl(s(z0))), MARK(dbl(s(z0))))
   MARK(add(x0, dbl(0))) -> c17(A__ADD(mark(x0), a__dbl(0)), MARK(dbl(0)))
   MARK(add(x0, dbl(nil))) -> c17(A__ADD(mark(x0), a__dbl(nil)), MARK(dbl(nil)))
   MARK(add(terms(z0), dbl(x1))) -> c17(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(sqr(z0), dbl(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(add(z0, z1), dbl(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(dbl(z0), dbl(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(first(z0, z1), dbl(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(0, dbl(x1))) -> c17(A__ADD(0, a__dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(x0, dbl(x1))) -> c17(MARK(dbl(x1)))
   MARK(add(cons(z0, z1), dbl(x1))) -> c17(MARK(dbl(x1)))
   MARK(add(recip(z0), dbl(x1))) -> c17(MARK(dbl(x1)))
   MARK(add(s(z0), dbl(x1))) -> c17(MARK(dbl(x1)))
   MARK(add(nil, dbl(x1))) -> c17(MARK(dbl(x1)))
   MARK(add(x0, first(x1, x2))) -> c17(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(x0, first(x1, terms(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(first(x1, terms(z0))))
   MARK(add(x0, first(x1, sqr(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(first(x1, sqr(z0))))
   MARK(add(x0, first(x1, add(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(first(x1, add(z0, z1))))
   MARK(add(x0, first(x1, dbl(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(first(x1, dbl(z0))))
   MARK(add(x0, first(x1, first(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1))))
   MARK(add(x0, first(x1, cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1))))
   MARK(add(x0, first(x1, recip(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(first(x1, recip(z0))))
   MARK(add(x0, first(x1, s(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(first(x1, s(z0))))
   MARK(add(x0, first(x1, 0))) -> c17(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0)))
   MARK(add(x0, first(x1, nil))) -> c17(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil)))
   MARK(add(x0, first(terms(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(first(terms(z0), x2)))
   MARK(add(x0, first(sqr(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(first(sqr(z0), x2)))
   MARK(add(x0, first(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(first(add(z0, z1), x2)))
   MARK(add(x0, first(dbl(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(first(dbl(z0), x2)))
   MARK(add(x0, first(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2)))
   MARK(add(x0, first(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2)))
   MARK(add(x0, first(recip(z0), x2))) -> c17(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(first(recip(z0), x2)))
   MARK(add(x0, first(s(z0), x2))) -> c17(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(first(s(z0), x2)))
   MARK(add(x0, first(0, x2))) -> c17(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2)))
   MARK(add(x0, first(nil, x2))) -> c17(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2)))
   MARK(add(terms(z0), first(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(sqr(z0), first(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(add(z0, z1), first(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(dbl(z0), first(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(first(z0, z1), first(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(cons(z0, z1), first(x1, x2))) -> c17(A__ADD(cons(mark(z0), z1), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(recip(z0), first(x1, x2))) -> c17(A__ADD(recip(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(s(z0), first(x1, x2))) -> c17(A__ADD(s(z0), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(0, first(x1, x2))) -> c17(A__ADD(0, a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(nil, first(x1, x2))) -> c17(A__ADD(nil, a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
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   MARK(add(x0, add(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(add(add(z0, z1), x2)))
   MARK(add(x0, add(dbl(z0), x2))) -> c17(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(add(dbl(z0), x2)))
   MARK(add(x0, add(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(add(first(z0, z1), x2)))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(add(cons(z0, z1), x2)))
   MARK(add(x0, add(recip(z0), x2))) -> c17(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(add(recip(z0), x2)))
   MARK(add(x0, add(s(z0), x2))) -> c17(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(add(s(z0), x2)))
   MARK(add(x0, add(0, x2))) -> c17(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(add(0, x2)))
   MARK(add(x0, add(nil, x2))) -> c17(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(add(nil, x2)))
   MARK(add(terms(z0), add(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2)))
   MARK(add(sqr(z0), add(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2)))
   MARK(add(add(z0, z1), add(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2)))
   MARK(add(dbl(z0), add(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2)))
   MARK(add(first(z0, z1), add(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2)))
   MARK(add(0, add(x1, x2))) -> c17(A__ADD(0, a__add(mark(x1), mark(x2))), MARK(add(x1, x2)))
   MARK(add(cons(z0, z1), add(x1, x2))) -> c17(MARK(add(x1, x2)))
   MARK(add(recip(z0), add(x1, x2))) -> c17(MARK(add(x1, x2)))
   MARK(add(s(z0), add(x1, x2))) -> c17(MARK(add(x1, x2)))
   MARK(add(nil, add(x1, x2))) -> c17(MARK(add(x1, x2)))
   MARK(add(x0, dbl(x1))) -> c17(A__ADD(mark(x0), dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(x0, dbl(terms(z0)))) -> c17(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0))))
   MARK(add(x0, dbl(sqr(z0)))) -> c17(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0))))
   MARK(add(x0, dbl(add(z0, z1)))) -> c17(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1))))
   MARK(add(x0, dbl(dbl(z0)))) -> c17(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0))))
   MARK(add(x0, dbl(first(z0, z1)))) -> c17(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1))))
   MARK(add(x0, dbl(cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1))))
   MARK(add(x0, dbl(recip(z0)))) -> c17(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0))))
   MARK(add(x0, dbl(s(z0)))) -> c17(A__ADD(mark(x0), a__dbl(s(z0))), MARK(dbl(s(z0))))
   MARK(add(x0, dbl(0))) -> c17(A__ADD(mark(x0), a__dbl(0)), MARK(dbl(0)))
   MARK(add(x0, dbl(nil))) -> c17(A__ADD(mark(x0), a__dbl(nil)), MARK(dbl(nil)))
   MARK(add(terms(z0), dbl(x1))) -> c17(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(sqr(z0), dbl(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(add(z0, z1), dbl(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(dbl(z0), dbl(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(first(z0, z1), dbl(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(0, dbl(x1))) -> c17(A__ADD(0, a__dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(x0, dbl(x1))) -> c17(MARK(dbl(x1)))
   MARK(add(cons(z0, z1), dbl(x1))) -> c17(MARK(dbl(x1)))
   MARK(add(recip(z0), dbl(x1))) -> c17(MARK(dbl(x1)))
   MARK(add(s(z0), dbl(x1))) -> c17(MARK(dbl(x1)))
   MARK(add(nil, dbl(x1))) -> c17(MARK(dbl(x1)))
   MARK(add(x0, first(x1, x2))) -> c17(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(x0, first(x1, terms(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(first(x1, terms(z0))))
   MARK(add(x0, first(x1, sqr(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(first(x1, sqr(z0))))
   MARK(add(x0, first(x1, add(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(first(x1, add(z0, z1))))
   MARK(add(x0, first(x1, dbl(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(first(x1, dbl(z0))))
   MARK(add(x0, first(x1, first(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1))))
   MARK(add(x0, first(x1, cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1))))
   MARK(add(x0, first(x1, recip(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(first(x1, recip(z0))))
   MARK(add(x0, first(x1, s(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(first(x1, s(z0))))
   MARK(add(x0, first(x1, 0))) -> c17(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0)))
   MARK(add(x0, first(x1, nil))) -> c17(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil)))
   MARK(add(x0, first(terms(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(first(terms(z0), x2)))
   MARK(add(x0, first(sqr(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(first(sqr(z0), x2)))
   MARK(add(x0, first(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(first(add(z0, z1), x2)))
   MARK(add(x0, first(dbl(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(first(dbl(z0), x2)))
   MARK(add(x0, first(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2)))
   MARK(add(x0, first(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2)))
   MARK(add(x0, first(recip(z0), x2))) -> c17(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(first(recip(z0), x2)))
   MARK(add(x0, first(s(z0), x2))) -> c17(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(first(s(z0), x2)))
   MARK(add(x0, first(0, x2))) -> c17(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2)))
   MARK(add(x0, first(nil, x2))) -> c17(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2)))
   MARK(add(terms(z0), first(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(sqr(z0), first(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(add(z0, z1), first(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(dbl(z0), first(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(first(z0, z1), first(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(cons(z0, z1), first(x1, x2))) -> c17(A__ADD(cons(mark(z0), z1), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(recip(z0), first(x1, x2))) -> c17(A__ADD(recip(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(s(z0), first(x1, x2))) -> c17(A__ADD(s(z0), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(0, first(x1, x2))) -> c17(A__ADD(0, a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(nil, first(x1, x2))) -> c17(A__ADD(nil, a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2


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

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

(150)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
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   MARK(add(nil, add(x1, x2))) -> c17(MARK(add(x1, x2)))
   MARK(add(x0, dbl(x1))) -> c17(A__ADD(mark(x0), dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(x0, dbl(terms(z0)))) -> c17(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0))))
   MARK(add(x0, dbl(sqr(z0)))) -> c17(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0))))
   MARK(add(x0, dbl(add(z0, z1)))) -> c17(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1))))
   MARK(add(x0, dbl(dbl(z0)))) -> c17(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0))))
   MARK(add(x0, dbl(first(z0, z1)))) -> c17(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1))))
   MARK(add(x0, dbl(cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1))))
   MARK(add(x0, dbl(recip(z0)))) -> c17(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0))))
   MARK(add(x0, dbl(s(z0)))) -> c17(A__ADD(mark(x0), a__dbl(s(z0))), MARK(dbl(s(z0))))
   MARK(add(x0, dbl(0))) -> c17(A__ADD(mark(x0), a__dbl(0)), MARK(dbl(0)))
   MARK(add(x0, dbl(nil))) -> c17(A__ADD(mark(x0), a__dbl(nil)), MARK(dbl(nil)))
   MARK(add(terms(z0), dbl(x1))) -> c17(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(sqr(z0), dbl(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(add(z0, z1), dbl(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(dbl(z0), dbl(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(first(z0, z1), dbl(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(0, dbl(x1))) -> c17(A__ADD(0, a__dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(x0, dbl(x1))) -> c17(MARK(dbl(x1)))
   MARK(add(cons(z0, z1), dbl(x1))) -> c17(MARK(dbl(x1)))
   MARK(add(recip(z0), dbl(x1))) -> c17(MARK(dbl(x1)))
   MARK(add(s(z0), dbl(x1))) -> c17(MARK(dbl(x1)))
   MARK(add(nil, dbl(x1))) -> c17(MARK(dbl(x1)))
   MARK(add(x0, first(x1, x2))) -> c17(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(x0, first(x1, terms(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(first(x1, terms(z0))))
   MARK(add(x0, first(x1, sqr(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(first(x1, sqr(z0))))
   MARK(add(x0, first(x1, add(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(first(x1, add(z0, z1))))
   MARK(add(x0, first(x1, dbl(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(first(x1, dbl(z0))))
   MARK(add(x0, first(x1, first(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1))))
   MARK(add(x0, first(x1, cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1))))
   MARK(add(x0, first(x1, recip(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(first(x1, recip(z0))))
   MARK(add(x0, first(x1, s(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(first(x1, s(z0))))
   MARK(add(x0, first(x1, 0))) -> c17(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0)))
   MARK(add(x0, first(x1, nil))) -> c17(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil)))
   MARK(add(x0, first(terms(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(first(terms(z0), x2)))
   MARK(add(x0, first(sqr(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(first(sqr(z0), x2)))
   MARK(add(x0, first(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(first(add(z0, z1), x2)))
   MARK(add(x0, first(dbl(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(first(dbl(z0), x2)))
   MARK(add(x0, first(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2)))
   MARK(add(x0, first(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2)))
   MARK(add(x0, first(recip(z0), x2))) -> c17(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(first(recip(z0), x2)))
   MARK(add(x0, first(s(z0), x2))) -> c17(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(first(s(z0), x2)))
   MARK(add(x0, first(0, x2))) -> c17(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2)))
   MARK(add(x0, first(nil, x2))) -> c17(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2)))
   MARK(add(terms(z0), first(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(sqr(z0), first(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(add(z0, z1), first(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(dbl(z0), first(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(first(z0, z1), first(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(0, first(x1, x2))) -> c17(A__ADD(0, a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(cons(z0, z1), first(x1, x2))) -> c17(MARK(first(x1, x2)))
   MARK(add(recip(z0), first(x1, x2))) -> c17(MARK(first(x1, x2)))
   MARK(add(s(z0), first(x1, x2))) -> c17(MARK(first(x1, x2)))
   MARK(add(nil, first(x1, x2))) -> c17(MARK(first(x1, x2)))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
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   MARK(add(x0, first(x1, nil))) -> c17(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil)))
   MARK(add(x0, first(terms(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(first(terms(z0), x2)))
   MARK(add(x0, first(sqr(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(first(sqr(z0), x2)))
   MARK(add(x0, first(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(first(add(z0, z1), x2)))
   MARK(add(x0, first(dbl(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(first(dbl(z0), x2)))
   MARK(add(x0, first(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2)))
   MARK(add(x0, first(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2)))
   MARK(add(x0, first(recip(z0), x2))) -> c17(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(first(recip(z0), x2)))
   MARK(add(x0, first(s(z0), x2))) -> c17(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(first(s(z0), x2)))
   MARK(add(x0, first(0, x2))) -> c17(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2)))
   MARK(add(x0, first(nil, x2))) -> c17(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2)))
   MARK(add(terms(z0), first(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(sqr(z0), first(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(add(z0, z1), first(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(dbl(z0), first(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(first(z0, z1), first(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(0, first(x1, x2))) -> c17(A__ADD(0, a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(cons(z0, z1), first(x1, x2))) -> c17(MARK(first(x1, x2)))
   MARK(add(recip(z0), first(x1, x2))) -> c17(MARK(first(x1, x2)))
   MARK(add(s(z0), first(x1, x2))) -> c17(MARK(first(x1, x2)))
   MARK(add(nil, first(x1, x2))) -> c17(MARK(first(x1, x2)))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2


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

(151) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) by 
   MARK(add(x0, cons(terms(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(cons(terms(z0), x2)))
   MARK(add(x0, cons(sqr(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(cons(sqr(z0), x2)))
   MARK(add(x0, cons(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(cons(add(z0, z1), x2)))
   MARK(add(x0, cons(dbl(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(cons(dbl(z0), x2)))
   MARK(add(x0, cons(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2)))
   MARK(add(x0, cons(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2)))
   MARK(add(x0, cons(recip(z0), x2))) -> c17(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(cons(recip(z0), x2)))
   MARK(add(x0, cons(s(z0), x2))) -> c17(A__ADD(mark(x0), cons(s(z0), x2)), MARK(cons(s(z0), x2)))
   MARK(add(x0, cons(0, x2))) -> c17(A__ADD(mark(x0), cons(0, x2)), MARK(cons(0, x2)))
   MARK(add(x0, cons(nil, x2))) -> c17(A__ADD(mark(x0), cons(nil, x2)), MARK(cons(nil, x2)))
   MARK(add(terms(z0), cons(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(sqr(z0), cons(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(add(z0, z1), cons(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(dbl(z0), cons(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(first(z0, z1), cons(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(cons(z0, z1), cons(x1, x2))) -> c17(A__ADD(cons(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(recip(z0), cons(x1, x2))) -> c17(A__ADD(recip(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(s(z0), cons(x1, x2))) -> c17(A__ADD(s(z0), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(0, cons(x1, x2))) -> c17(A__ADD(0, cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(nil, cons(x1, x2))) -> c17(A__ADD(nil, cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(x0, cons(x1, x2))) -> c17(MARK(cons(x1, x2)))

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

(152)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
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   MARK(add(x0, first(x1, s(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(first(x1, s(z0))))
   MARK(add(x0, first(x1, 0))) -> c17(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0)))
   MARK(add(x0, first(x1, nil))) -> c17(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil)))
   MARK(add(x0, first(terms(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(first(terms(z0), x2)))
   MARK(add(x0, first(sqr(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(first(sqr(z0), x2)))
   MARK(add(x0, first(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(first(add(z0, z1), x2)))
   MARK(add(x0, first(dbl(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(first(dbl(z0), x2)))
   MARK(add(x0, first(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2)))
   MARK(add(x0, first(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2)))
   MARK(add(x0, first(recip(z0), x2))) -> c17(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(first(recip(z0), x2)))
   MARK(add(x0, first(s(z0), x2))) -> c17(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(first(s(z0), x2)))
   MARK(add(x0, first(0, x2))) -> c17(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2)))
   MARK(add(x0, first(nil, x2))) -> c17(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2)))
   MARK(add(terms(z0), first(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(sqr(z0), first(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(add(z0, z1), first(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(dbl(z0), first(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(first(z0, z1), first(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(0, first(x1, x2))) -> c17(A__ADD(0, a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(cons(z0, z1), first(x1, x2))) -> c17(MARK(first(x1, x2)))
   MARK(add(recip(z0), first(x1, x2))) -> c17(MARK(first(x1, x2)))
   MARK(add(s(z0), first(x1, x2))) -> c17(MARK(first(x1, x2)))
   MARK(add(nil, first(x1, x2))) -> c17(MARK(first(x1, x2)))
   MARK(add(x0, cons(terms(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(cons(terms(z0), x2)))
   MARK(add(x0, cons(sqr(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(cons(sqr(z0), x2)))
   MARK(add(x0, cons(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(cons(add(z0, z1), x2)))
   MARK(add(x0, cons(dbl(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(cons(dbl(z0), x2)))
   MARK(add(x0, cons(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2)))
   MARK(add(x0, cons(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2)))
   MARK(add(x0, cons(recip(z0), x2))) -> c17(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(cons(recip(z0), x2)))
   MARK(add(x0, cons(s(z0), x2))) -> c17(A__ADD(mark(x0), cons(s(z0), x2)), MARK(cons(s(z0), x2)))
   MARK(add(x0, cons(0, x2))) -> c17(A__ADD(mark(x0), cons(0, x2)), MARK(cons(0, x2)))
   MARK(add(x0, cons(nil, x2))) -> c17(A__ADD(mark(x0), cons(nil, x2)), MARK(cons(nil, x2)))
   MARK(add(terms(z0), cons(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(sqr(z0), cons(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(add(z0, z1), cons(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(dbl(z0), cons(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(first(z0, z1), cons(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(cons(z0, z1), cons(x1, x2))) -> c17(A__ADD(cons(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(recip(z0), cons(x1, x2))) -> c17(A__ADD(recip(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(s(z0), cons(x1, x2))) -> c17(A__ADD(s(z0), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(0, cons(x1, x2))) -> c17(A__ADD(0, cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(nil, cons(x1, x2))) -> c17(A__ADD(nil, cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(x0, cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
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   MARK(add(x0, first(recip(z0), x2))) -> c17(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(first(recip(z0), x2)))
   MARK(add(x0, first(s(z0), x2))) -> c17(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(first(s(z0), x2)))
   MARK(add(x0, first(0, x2))) -> c17(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2)))
   MARK(add(x0, first(nil, x2))) -> c17(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2)))
   MARK(add(terms(z0), first(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(sqr(z0), first(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(add(z0, z1), first(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(dbl(z0), first(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(first(z0, z1), first(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(0, first(x1, x2))) -> c17(A__ADD(0, a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(cons(z0, z1), first(x1, x2))) -> c17(MARK(first(x1, x2)))
   MARK(add(recip(z0), first(x1, x2))) -> c17(MARK(first(x1, x2)))
   MARK(add(s(z0), first(x1, x2))) -> c17(MARK(first(x1, x2)))
   MARK(add(nil, first(x1, x2))) -> c17(MARK(first(x1, x2)))
   MARK(add(x0, cons(terms(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(cons(terms(z0), x2)))
   MARK(add(x0, cons(sqr(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(cons(sqr(z0), x2)))
   MARK(add(x0, cons(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(cons(add(z0, z1), x2)))
   MARK(add(x0, cons(dbl(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(cons(dbl(z0), x2)))
   MARK(add(x0, cons(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2)))
   MARK(add(x0, cons(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2)))
   MARK(add(x0, cons(recip(z0), x2))) -> c17(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(cons(recip(z0), x2)))
   MARK(add(x0, cons(s(z0), x2))) -> c17(A__ADD(mark(x0), cons(s(z0), x2)), MARK(cons(s(z0), x2)))
   MARK(add(x0, cons(0, x2))) -> c17(A__ADD(mark(x0), cons(0, x2)), MARK(cons(0, x2)))
   MARK(add(x0, cons(nil, x2))) -> c17(A__ADD(mark(x0), cons(nil, x2)), MARK(cons(nil, x2)))
   MARK(add(terms(z0), cons(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(sqr(z0), cons(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(add(z0, z1), cons(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(dbl(z0), cons(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(first(z0, z1), cons(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(cons(z0, z1), cons(x1, x2))) -> c17(A__ADD(cons(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(recip(z0), cons(x1, x2))) -> c17(A__ADD(recip(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(s(z0), cons(x1, x2))) -> c17(A__ADD(s(z0), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(0, cons(x1, x2))) -> c17(A__ADD(0, cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(nil, cons(x1, x2))) -> c17(A__ADD(nil, cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(x0, cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2


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

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

(154)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0))
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   MARK(add(x0, first(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2)))
   MARK(add(x0, first(recip(z0), x2))) -> c17(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(first(recip(z0), x2)))
   MARK(add(x0, first(s(z0), x2))) -> c17(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(first(s(z0), x2)))
   MARK(add(x0, first(0, x2))) -> c17(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2)))
   MARK(add(x0, first(nil, x2))) -> c17(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2)))
   MARK(add(terms(z0), first(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(sqr(z0), first(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(add(z0, z1), first(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(dbl(z0), first(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(first(z0, z1), first(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(0, first(x1, x2))) -> c17(A__ADD(0, a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(cons(z0, z1), first(x1, x2))) -> c17(MARK(first(x1, x2)))
   MARK(add(recip(z0), first(x1, x2))) -> c17(MARK(first(x1, x2)))
   MARK(add(s(z0), first(x1, x2))) -> c17(MARK(first(x1, x2)))
   MARK(add(nil, first(x1, x2))) -> c17(MARK(first(x1, x2)))
   MARK(add(x0, cons(terms(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(cons(terms(z0), x2)))
   MARK(add(x0, cons(sqr(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(cons(sqr(z0), x2)))
   MARK(add(x0, cons(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(cons(add(z0, z1), x2)))
   MARK(add(x0, cons(dbl(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(cons(dbl(z0), x2)))
   MARK(add(x0, cons(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2)))
   MARK(add(x0, cons(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2)))
   MARK(add(x0, cons(recip(z0), x2))) -> c17(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(cons(recip(z0), x2)))
   MARK(add(x0, cons(s(z0), x2))) -> c17(A__ADD(mark(x0), cons(s(z0), x2)), MARK(cons(s(z0), x2)))
   MARK(add(x0, cons(0, x2))) -> c17(A__ADD(mark(x0), cons(0, x2)), MARK(cons(0, x2)))
   MARK(add(x0, cons(nil, x2))) -> c17(A__ADD(mark(x0), cons(nil, x2)), MARK(cons(nil, x2)))
   MARK(add(terms(z0), cons(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(sqr(z0), cons(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(add(z0, z1), cons(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(dbl(z0), cons(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(first(z0, z1), cons(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(0, cons(x1, x2))) -> c17(A__ADD(0, cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(x0, cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
   MARK(add(cons(z0, z1), cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
   MARK(add(recip(z0), cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
   MARK(add(s(z0), cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
   MARK(add(nil, cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2))))
   MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0))
   MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0))
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   MARK(add(recip(z0), first(x1, x2))) -> c17(MARK(first(x1, x2)))
   MARK(add(s(z0), first(x1, x2))) -> c17(MARK(first(x1, x2)))
   MARK(add(nil, first(x1, x2))) -> c17(MARK(first(x1, x2)))
   MARK(add(x0, cons(terms(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(cons(terms(z0), x2)))
   MARK(add(x0, cons(sqr(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(cons(sqr(z0), x2)))
   MARK(add(x0, cons(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(cons(add(z0, z1), x2)))
   MARK(add(x0, cons(dbl(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(cons(dbl(z0), x2)))
   MARK(add(x0, cons(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2)))
   MARK(add(x0, cons(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2)))
   MARK(add(x0, cons(recip(z0), x2))) -> c17(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(cons(recip(z0), x2)))
   MARK(add(x0, cons(s(z0), x2))) -> c17(A__ADD(mark(x0), cons(s(z0), x2)), MARK(cons(s(z0), x2)))
   MARK(add(x0, cons(0, x2))) -> c17(A__ADD(mark(x0), cons(0, x2)), MARK(cons(0, x2)))
   MARK(add(x0, cons(nil, x2))) -> c17(A__ADD(mark(x0), cons(nil, x2)), MARK(cons(nil, x2)))
   MARK(add(terms(z0), cons(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(sqr(z0), cons(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(add(z0, z1), cons(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(dbl(z0), cons(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(first(z0, z1), cons(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(0, cons(x1, x2))) -> c17(A__ADD(0, cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(x0, cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
   MARK(add(cons(z0, z1), cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
   MARK(add(recip(z0), cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
   MARK(add(s(z0), cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
   MARK(add(nil, cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2


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

(155) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) by 
   MARK(add(x0, recip(terms(z0)))) -> c17(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(recip(terms(z0))))
   MARK(add(x0, recip(sqr(z0)))) -> c17(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(recip(sqr(z0))))
   MARK(add(x0, recip(add(z0, z1)))) -> c17(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(recip(add(z0, z1))))
   MARK(add(x0, recip(dbl(z0)))) -> c17(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(recip(dbl(z0))))
   MARK(add(x0, recip(first(z0, z1)))) -> c17(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(recip(first(z0, z1))))
   MARK(add(x0, recip(cons(z0, z1)))) -> c17(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(recip(cons(z0, z1))))
   MARK(add(x0, recip(recip(z0)))) -> c17(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(recip(recip(z0))))
   MARK(add(x0, recip(s(z0)))) -> c17(A__ADD(mark(x0), recip(s(z0))), MARK(recip(s(z0))))
   MARK(add(x0, recip(0))) -> c17(A__ADD(mark(x0), recip(0)), MARK(recip(0)))
   MARK(add(x0, recip(nil))) -> c17(A__ADD(mark(x0), recip(nil)), MARK(recip(nil)))
   MARK(add(terms(z0), recip(x1))) -> c17(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(sqr(z0), recip(x1))) -> c17(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(add(z0, z1), recip(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(dbl(z0), recip(x1))) -> c17(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(first(z0, z1), recip(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(cons(z0, z1), recip(x1))) -> c17(A__ADD(cons(mark(z0), z1), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(recip(z0), recip(x1))) -> c17(A__ADD(recip(mark(z0)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(s(z0), recip(x1))) -> c17(A__ADD(s(z0), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(0, recip(x1))) -> c17(A__ADD(0, recip(mark(x1))), MARK(recip(x1)))
   MARK(add(nil, recip(x1))) -> c17(A__ADD(nil, recip(mark(x1))), MARK(recip(x1)))
   MARK(add(x0, recip(x1))) -> c17(MARK(recip(x1)))

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

(156)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
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   MARK(add(x0, first(sqr(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(first(sqr(z0), x2)))
   MARK(add(x0, first(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(first(add(z0, z1), x2)))
   MARK(add(x0, first(dbl(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(first(dbl(z0), x2)))
   MARK(add(x0, first(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2)))
   MARK(add(x0, first(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2)))
   MARK(add(x0, first(recip(z0), x2))) -> c17(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(first(recip(z0), x2)))
   MARK(add(x0, first(s(z0), x2))) -> c17(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(first(s(z0), x2)))
   MARK(add(x0, first(0, x2))) -> c17(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2)))
   MARK(add(x0, first(nil, x2))) -> c17(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2)))
   MARK(add(terms(z0), first(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(sqr(z0), first(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(add(z0, z1), first(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(dbl(z0), first(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(first(z0, z1), first(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(0, first(x1, x2))) -> c17(A__ADD(0, a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(cons(z0, z1), first(x1, x2))) -> c17(MARK(first(x1, x2)))
   MARK(add(recip(z0), first(x1, x2))) -> c17(MARK(first(x1, x2)))
   MARK(add(s(z0), first(x1, x2))) -> c17(MARK(first(x1, x2)))
   MARK(add(nil, first(x1, x2))) -> c17(MARK(first(x1, x2)))
   MARK(add(x0, cons(terms(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(cons(terms(z0), x2)))
   MARK(add(x0, cons(sqr(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(cons(sqr(z0), x2)))
   MARK(add(x0, cons(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(cons(add(z0, z1), x2)))
   MARK(add(x0, cons(dbl(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(cons(dbl(z0), x2)))
   MARK(add(x0, cons(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2)))
   MARK(add(x0, cons(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2)))
   MARK(add(x0, cons(recip(z0), x2))) -> c17(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(cons(recip(z0), x2)))
   MARK(add(x0, cons(s(z0), x2))) -> c17(A__ADD(mark(x0), cons(s(z0), x2)), MARK(cons(s(z0), x2)))
   MARK(add(x0, cons(0, x2))) -> c17(A__ADD(mark(x0), cons(0, x2)), MARK(cons(0, x2)))
   MARK(add(x0, cons(nil, x2))) -> c17(A__ADD(mark(x0), cons(nil, x2)), MARK(cons(nil, x2)))
   MARK(add(terms(z0), cons(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(sqr(z0), cons(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(add(z0, z1), cons(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(dbl(z0), cons(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(first(z0, z1), cons(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(0, cons(x1, x2))) -> c17(A__ADD(0, cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(x0, cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
   MARK(add(cons(z0, z1), cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
   MARK(add(recip(z0), cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
   MARK(add(s(z0), cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
   MARK(add(nil, cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
   MARK(add(x0, recip(terms(z0)))) -> c17(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(recip(terms(z0))))
   MARK(add(x0, recip(sqr(z0)))) -> c17(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(recip(sqr(z0))))
   MARK(add(x0, recip(add(z0, z1)))) -> c17(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(recip(add(z0, z1))))
   MARK(add(x0, recip(dbl(z0)))) -> c17(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(recip(dbl(z0))))
   MARK(add(x0, recip(first(z0, z1)))) -> c17(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(recip(first(z0, z1))))
   MARK(add(x0, recip(cons(z0, z1)))) -> c17(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(recip(cons(z0, z1))))
   MARK(add(x0, recip(recip(z0)))) -> c17(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(recip(recip(z0))))
   MARK(add(x0, recip(s(z0)))) -> c17(A__ADD(mark(x0), recip(s(z0))), MARK(recip(s(z0))))
   MARK(add(x0, recip(0))) -> c17(A__ADD(mark(x0), recip(0)), MARK(recip(0)))
   MARK(add(x0, recip(nil))) -> c17(A__ADD(mark(x0), recip(nil)), MARK(recip(nil)))
   MARK(add(terms(z0), recip(x1))) -> c17(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(sqr(z0), recip(x1))) -> c17(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(add(z0, z1), recip(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(dbl(z0), recip(x1))) -> c17(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(first(z0, z1), recip(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(cons(z0, z1), recip(x1))) -> c17(A__ADD(cons(mark(z0), z1), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(recip(z0), recip(x1))) -> c17(A__ADD(recip(mark(z0)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(s(z0), recip(x1))) -> c17(A__ADD(s(z0), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(0, recip(x1))) -> c17(A__ADD(0, recip(mark(x1))), MARK(recip(x1)))
   MARK(add(nil, recip(x1))) -> c17(A__ADD(nil, recip(mark(x1))), MARK(recip(x1)))
   MARK(add(x0, recip(x1))) -> c17(MARK(recip(x1)))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
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   MARK(add(x0, first(x1, recip(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(first(x1, recip(z0))))
   MARK(add(x0, first(x1, s(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(first(x1, s(z0))))
   MARK(add(x0, first(x1, 0))) -> c17(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0)))
   MARK(add(x0, first(x1, nil))) -> c17(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil)))
   MARK(add(x0, first(terms(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(first(terms(z0), x2)))
   MARK(add(x0, first(sqr(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(first(sqr(z0), x2)))
   MARK(add(x0, first(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(first(add(z0, z1), x2)))
   MARK(add(x0, first(dbl(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(first(dbl(z0), x2)))
   MARK(add(x0, first(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2)))
   MARK(add(x0, first(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2)))
   MARK(add(x0, first(recip(z0), x2))) -> c17(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(first(recip(z0), x2)))
   MARK(add(x0, first(s(z0), x2))) -> c17(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(first(s(z0), x2)))
   MARK(add(x0, first(0, x2))) -> c17(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2)))
   MARK(add(x0, first(nil, x2))) -> c17(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2)))
   MARK(add(terms(z0), first(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(sqr(z0), first(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(add(z0, z1), first(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(dbl(z0), first(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(first(z0, z1), first(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(0, first(x1, x2))) -> c17(A__ADD(0, a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(cons(z0, z1), first(x1, x2))) -> c17(MARK(first(x1, x2)))
   MARK(add(recip(z0), first(x1, x2))) -> c17(MARK(first(x1, x2)))
   MARK(add(s(z0), first(x1, x2))) -> c17(MARK(first(x1, x2)))
   MARK(add(nil, first(x1, x2))) -> c17(MARK(first(x1, x2)))
   MARK(add(x0, cons(terms(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(cons(terms(z0), x2)))
   MARK(add(x0, cons(sqr(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(cons(sqr(z0), x2)))
   MARK(add(x0, cons(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(cons(add(z0, z1), x2)))
   MARK(add(x0, cons(dbl(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(cons(dbl(z0), x2)))
   MARK(add(x0, cons(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2)))
   MARK(add(x0, cons(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2)))
   MARK(add(x0, cons(recip(z0), x2))) -> c17(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(cons(recip(z0), x2)))
   MARK(add(x0, cons(s(z0), x2))) -> c17(A__ADD(mark(x0), cons(s(z0), x2)), MARK(cons(s(z0), x2)))
   MARK(add(x0, cons(0, x2))) -> c17(A__ADD(mark(x0), cons(0, x2)), MARK(cons(0, x2)))
   MARK(add(x0, cons(nil, x2))) -> c17(A__ADD(mark(x0), cons(nil, x2)), MARK(cons(nil, x2)))
   MARK(add(terms(z0), cons(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(sqr(z0), cons(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(add(z0, z1), cons(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(dbl(z0), cons(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(first(z0, z1), cons(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(0, cons(x1, x2))) -> c17(A__ADD(0, cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(x0, cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
   MARK(add(cons(z0, z1), cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
   MARK(add(recip(z0), cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
   MARK(add(s(z0), cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
   MARK(add(nil, cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
   MARK(add(x0, recip(terms(z0)))) -> c17(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(recip(terms(z0))))
   MARK(add(x0, recip(sqr(z0)))) -> c17(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(recip(sqr(z0))))
   MARK(add(x0, recip(add(z0, z1)))) -> c17(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(recip(add(z0, z1))))
   MARK(add(x0, recip(dbl(z0)))) -> c17(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(recip(dbl(z0))))
   MARK(add(x0, recip(first(z0, z1)))) -> c17(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(recip(first(z0, z1))))
   MARK(add(x0, recip(cons(z0, z1)))) -> c17(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(recip(cons(z0, z1))))
   MARK(add(x0, recip(recip(z0)))) -> c17(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(recip(recip(z0))))
   MARK(add(x0, recip(s(z0)))) -> c17(A__ADD(mark(x0), recip(s(z0))), MARK(recip(s(z0))))
   MARK(add(x0, recip(0))) -> c17(A__ADD(mark(x0), recip(0)), MARK(recip(0)))
   MARK(add(x0, recip(nil))) -> c17(A__ADD(mark(x0), recip(nil)), MARK(recip(nil)))
   MARK(add(terms(z0), recip(x1))) -> c17(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(sqr(z0), recip(x1))) -> c17(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(add(z0, z1), recip(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(dbl(z0), recip(x1))) -> c17(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(first(z0, z1), recip(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(cons(z0, z1), recip(x1))) -> c17(A__ADD(cons(mark(z0), z1), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(recip(z0), recip(x1))) -> c17(A__ADD(recip(mark(z0)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(s(z0), recip(x1))) -> c17(A__ADD(s(z0), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(0, recip(x1))) -> c17(A__ADD(0, recip(mark(x1))), MARK(recip(x1)))
   MARK(add(nil, recip(x1))) -> c17(A__ADD(nil, recip(mark(x1))), MARK(recip(x1)))
   MARK(add(x0, recip(x1))) -> c17(MARK(recip(x1)))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2


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

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

(158)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
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   MARK(add(x0, dbl(0))) -> c17(A__ADD(mark(x0), a__dbl(0)), MARK(dbl(0)))
   MARK(add(x0, dbl(nil))) -> c17(A__ADD(mark(x0), a__dbl(nil)), MARK(dbl(nil)))
   MARK(add(terms(z0), dbl(x1))) -> c17(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(sqr(z0), dbl(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(add(z0, z1), dbl(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(dbl(z0), dbl(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(first(z0, z1), dbl(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(0, dbl(x1))) -> c17(A__ADD(0, a__dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(x0, dbl(x1))) -> c17(MARK(dbl(x1)))
   MARK(add(cons(z0, z1), dbl(x1))) -> c17(MARK(dbl(x1)))
   MARK(add(recip(z0), dbl(x1))) -> c17(MARK(dbl(x1)))
   MARK(add(s(z0), dbl(x1))) -> c17(MARK(dbl(x1)))
   MARK(add(nil, dbl(x1))) -> c17(MARK(dbl(x1)))
   MARK(add(x0, first(x1, x2))) -> c17(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(x0, first(x1, terms(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(first(x1, terms(z0))))
   MARK(add(x0, first(x1, sqr(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(first(x1, sqr(z0))))
   MARK(add(x0, first(x1, add(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(first(x1, add(z0, z1))))
   MARK(add(x0, first(x1, dbl(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(first(x1, dbl(z0))))
   MARK(add(x0, first(x1, first(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1))))
   MARK(add(x0, first(x1, cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1))))
   MARK(add(x0, first(x1, recip(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(first(x1, recip(z0))))
   MARK(add(x0, first(x1, s(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(first(x1, s(z0))))
   MARK(add(x0, first(x1, 0))) -> c17(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0)))
   MARK(add(x0, first(x1, nil))) -> c17(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil)))
   MARK(add(x0, first(terms(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(first(terms(z0), x2)))
   MARK(add(x0, first(sqr(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(first(sqr(z0), x2)))
   MARK(add(x0, first(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(first(add(z0, z1), x2)))
   MARK(add(x0, first(dbl(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(first(dbl(z0), x2)))
   MARK(add(x0, first(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2)))
   MARK(add(x0, first(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2)))
   MARK(add(x0, first(recip(z0), x2))) -> c17(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(first(recip(z0), x2)))
   MARK(add(x0, first(s(z0), x2))) -> c17(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(first(s(z0), x2)))
   MARK(add(x0, first(0, x2))) -> c17(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2)))
   MARK(add(x0, first(nil, x2))) -> c17(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2)))
   MARK(add(terms(z0), first(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(sqr(z0), first(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(add(z0, z1), first(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(dbl(z0), first(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(first(z0, z1), first(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(0, first(x1, x2))) -> c17(A__ADD(0, a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(cons(z0, z1), first(x1, x2))) -> c17(MARK(first(x1, x2)))
   MARK(add(recip(z0), first(x1, x2))) -> c17(MARK(first(x1, x2)))
   MARK(add(s(z0), first(x1, x2))) -> c17(MARK(first(x1, x2)))
   MARK(add(nil, first(x1, x2))) -> c17(MARK(first(x1, x2)))
   MARK(add(x0, cons(terms(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(cons(terms(z0), x2)))
   MARK(add(x0, cons(sqr(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(cons(sqr(z0), x2)))
   MARK(add(x0, cons(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(cons(add(z0, z1), x2)))
   MARK(add(x0, cons(dbl(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(cons(dbl(z0), x2)))
   MARK(add(x0, cons(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2)))
   MARK(add(x0, cons(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2)))
   MARK(add(x0, cons(recip(z0), x2))) -> c17(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(cons(recip(z0), x2)))
   MARK(add(x0, cons(s(z0), x2))) -> c17(A__ADD(mark(x0), cons(s(z0), x2)), MARK(cons(s(z0), x2)))
   MARK(add(x0, cons(0, x2))) -> c17(A__ADD(mark(x0), cons(0, x2)), MARK(cons(0, x2)))
   MARK(add(x0, cons(nil, x2))) -> c17(A__ADD(mark(x0), cons(nil, x2)), MARK(cons(nil, x2)))
   MARK(add(terms(z0), cons(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(sqr(z0), cons(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(add(z0, z1), cons(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(dbl(z0), cons(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(first(z0, z1), cons(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(0, cons(x1, x2))) -> c17(A__ADD(0, cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(x0, cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
   MARK(add(cons(z0, z1), cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
   MARK(add(recip(z0), cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
   MARK(add(s(z0), cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
   MARK(add(nil, cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
   MARK(add(x0, recip(terms(z0)))) -> c17(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(recip(terms(z0))))
   MARK(add(x0, recip(sqr(z0)))) -> c17(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(recip(sqr(z0))))
   MARK(add(x0, recip(add(z0, z1)))) -> c17(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(recip(add(z0, z1))))
   MARK(add(x0, recip(dbl(z0)))) -> c17(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(recip(dbl(z0))))
   MARK(add(x0, recip(first(z0, z1)))) -> c17(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(recip(first(z0, z1))))
   MARK(add(x0, recip(cons(z0, z1)))) -> c17(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(recip(cons(z0, z1))))
   MARK(add(x0, recip(recip(z0)))) -> c17(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(recip(recip(z0))))
   MARK(add(x0, recip(s(z0)))) -> c17(A__ADD(mark(x0), recip(s(z0))), MARK(recip(s(z0))))
   MARK(add(x0, recip(0))) -> c17(A__ADD(mark(x0), recip(0)), MARK(recip(0)))
   MARK(add(x0, recip(nil))) -> c17(A__ADD(mark(x0), recip(nil)), MARK(recip(nil)))
   MARK(add(terms(z0), recip(x1))) -> c17(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(sqr(z0), recip(x1))) -> c17(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(add(z0, z1), recip(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(dbl(z0), recip(x1))) -> c17(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(first(z0, z1), recip(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(0, recip(x1))) -> c17(A__ADD(0, recip(mark(x1))), MARK(recip(x1)))
   MARK(add(x0, recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(cons(z0, z1), recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(recip(z0), recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(s(z0), recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(nil, recip(x1))) -> c17(MARK(recip(x1)))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
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   MARK(add(x0, dbl(recip(z0)))) -> c17(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0))))
   MARK(add(x0, dbl(s(z0)))) -> c17(A__ADD(mark(x0), a__dbl(s(z0))), MARK(dbl(s(z0))))
   MARK(add(x0, dbl(0))) -> c17(A__ADD(mark(x0), a__dbl(0)), MARK(dbl(0)))
   MARK(add(x0, dbl(nil))) -> c17(A__ADD(mark(x0), a__dbl(nil)), MARK(dbl(nil)))
   MARK(add(terms(z0), dbl(x1))) -> c17(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(sqr(z0), dbl(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(add(z0, z1), dbl(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(dbl(z0), dbl(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(first(z0, z1), dbl(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(0, dbl(x1))) -> c17(A__ADD(0, a__dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(x0, dbl(x1))) -> c17(MARK(dbl(x1)))
   MARK(add(cons(z0, z1), dbl(x1))) -> c17(MARK(dbl(x1)))
   MARK(add(recip(z0), dbl(x1))) -> c17(MARK(dbl(x1)))
   MARK(add(s(z0), dbl(x1))) -> c17(MARK(dbl(x1)))
   MARK(add(nil, dbl(x1))) -> c17(MARK(dbl(x1)))
   MARK(add(x0, first(x1, x2))) -> c17(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(x0, first(x1, terms(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(first(x1, terms(z0))))
   MARK(add(x0, first(x1, sqr(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(first(x1, sqr(z0))))
   MARK(add(x0, first(x1, add(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(first(x1, add(z0, z1))))
   MARK(add(x0, first(x1, dbl(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(first(x1, dbl(z0))))
   MARK(add(x0, first(x1, first(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1))))
   MARK(add(x0, first(x1, cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1))))
   MARK(add(x0, first(x1, recip(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(first(x1, recip(z0))))
   MARK(add(x0, first(x1, s(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(first(x1, s(z0))))
   MARK(add(x0, first(x1, 0))) -> c17(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0)))
   MARK(add(x0, first(x1, nil))) -> c17(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil)))
   MARK(add(x0, first(terms(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(first(terms(z0), x2)))
   MARK(add(x0, first(sqr(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(first(sqr(z0), x2)))
   MARK(add(x0, first(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(first(add(z0, z1), x2)))
   MARK(add(x0, first(dbl(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(first(dbl(z0), x2)))
   MARK(add(x0, first(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2)))
   MARK(add(x0, first(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2)))
   MARK(add(x0, first(recip(z0), x2))) -> c17(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(first(recip(z0), x2)))
   MARK(add(x0, first(s(z0), x2))) -> c17(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(first(s(z0), x2)))
   MARK(add(x0, first(0, x2))) -> c17(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2)))
   MARK(add(x0, first(nil, x2))) -> c17(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2)))
   MARK(add(terms(z0), first(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(sqr(z0), first(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(add(z0, z1), first(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(dbl(z0), first(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(first(z0, z1), first(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(0, first(x1, x2))) -> c17(A__ADD(0, a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(cons(z0, z1), first(x1, x2))) -> c17(MARK(first(x1, x2)))
   MARK(add(recip(z0), first(x1, x2))) -> c17(MARK(first(x1, x2)))
   MARK(add(s(z0), first(x1, x2))) -> c17(MARK(first(x1, x2)))
   MARK(add(nil, first(x1, x2))) -> c17(MARK(first(x1, x2)))
   MARK(add(x0, cons(terms(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(cons(terms(z0), x2)))
   MARK(add(x0, cons(sqr(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(cons(sqr(z0), x2)))
   MARK(add(x0, cons(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(cons(add(z0, z1), x2)))
   MARK(add(x0, cons(dbl(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(cons(dbl(z0), x2)))
   MARK(add(x0, cons(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2)))
   MARK(add(x0, cons(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2)))
   MARK(add(x0, cons(recip(z0), x2))) -> c17(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(cons(recip(z0), x2)))
   MARK(add(x0, cons(s(z0), x2))) -> c17(A__ADD(mark(x0), cons(s(z0), x2)), MARK(cons(s(z0), x2)))
   MARK(add(x0, cons(0, x2))) -> c17(A__ADD(mark(x0), cons(0, x2)), MARK(cons(0, x2)))
   MARK(add(x0, cons(nil, x2))) -> c17(A__ADD(mark(x0), cons(nil, x2)), MARK(cons(nil, x2)))
   MARK(add(terms(z0), cons(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(sqr(z0), cons(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(add(z0, z1), cons(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(dbl(z0), cons(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(first(z0, z1), cons(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(0, cons(x1, x2))) -> c17(A__ADD(0, cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(x0, cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
   MARK(add(cons(z0, z1), cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
   MARK(add(recip(z0), cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
   MARK(add(s(z0), cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
   MARK(add(nil, cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
   MARK(add(x0, recip(terms(z0)))) -> c17(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(recip(terms(z0))))
   MARK(add(x0, recip(sqr(z0)))) -> c17(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(recip(sqr(z0))))
   MARK(add(x0, recip(add(z0, z1)))) -> c17(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(recip(add(z0, z1))))
   MARK(add(x0, recip(dbl(z0)))) -> c17(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(recip(dbl(z0))))
   MARK(add(x0, recip(first(z0, z1)))) -> c17(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(recip(first(z0, z1))))
   MARK(add(x0, recip(cons(z0, z1)))) -> c17(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(recip(cons(z0, z1))))
   MARK(add(x0, recip(recip(z0)))) -> c17(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(recip(recip(z0))))
   MARK(add(x0, recip(s(z0)))) -> c17(A__ADD(mark(x0), recip(s(z0))), MARK(recip(s(z0))))
   MARK(add(x0, recip(0))) -> c17(A__ADD(mark(x0), recip(0)), MARK(recip(0)))
   MARK(add(x0, recip(nil))) -> c17(A__ADD(mark(x0), recip(nil)), MARK(recip(nil)))
   MARK(add(terms(z0), recip(x1))) -> c17(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(sqr(z0), recip(x1))) -> c17(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(add(z0, z1), recip(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(dbl(z0), recip(x1))) -> c17(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(first(z0, z1), recip(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(0, recip(x1))) -> c17(A__ADD(0, recip(mark(x1))), MARK(recip(x1)))
   MARK(add(x0, recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(cons(z0, z1), recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(recip(z0), recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(s(z0), recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(nil, recip(x1))) -> c17(MARK(recip(x1)))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2


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

(159) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) by 
   MARK(add(terms(x0), terms(z0))) -> c17(A__ADD(a__terms(mark(x0)), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(terms(x0), sqr(z0))) -> c17(A__ADD(a__terms(mark(x0)), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(terms(x0), add(z0, z1))) -> c17(A__ADD(a__terms(mark(x0)), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(terms(x0), dbl(z0))) -> c17(A__ADD(a__terms(mark(x0)), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(terms(x0), first(z0, z1))) -> c17(A__ADD(a__terms(mark(x0)), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(terms(x0), cons(z0, z1))) -> c17(A__ADD(a__terms(mark(x0)), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(terms(x0), recip(z0))) -> c17(A__ADD(a__terms(mark(x0)), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(terms(x0), s(z0))) -> c17(A__ADD(a__terms(mark(x0)), s(z0)), MARK(s(z0)))
   MARK(add(terms(x0), 0)) -> c17(A__ADD(a__terms(mark(x0)), 0), MARK(0))
   MARK(add(terms(x0), nil)) -> c17(A__ADD(a__terms(mark(x0)), nil), MARK(nil))
   MARK(add(terms(x0), x1)) -> c17(A__ADD(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0)))), mark(x1)), MARK(x1))
   MARK(add(terms(x0), x1)) -> c17(A__ADD(terms(mark(x0)), mark(x1)), MARK(x1))
   MARK(add(terms(terms(z0)), x1)) -> c17(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(terms(sqr(z0)), x1)) -> c17(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(terms(add(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(terms(dbl(z0)), x1)) -> c17(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(terms(first(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(terms(cons(z0, z1)), x1)) -> c17(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(x1))
   MARK(add(terms(recip(z0)), x1)) -> c17(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(terms(s(z0)), x1)) -> c17(A__ADD(a__terms(s(z0)), mark(x1)), MARK(x1))
   MARK(add(terms(0), x1)) -> c17(A__ADD(a__terms(0), mark(x1)), MARK(x1))
   MARK(add(terms(nil), x1)) -> c17(A__ADD(a__terms(nil), mark(x1)), MARK(x1))

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

(160)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
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   MARK(add(cons(z0, z1), dbl(x1))) -> c17(MARK(dbl(x1)))
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   MARK(add(x0, first(x1, add(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(first(x1, add(z0, z1))))
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   MARK(add(x0, first(x1, first(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1))))
   MARK(add(x0, first(x1, cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1))))
   MARK(add(x0, first(x1, recip(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(first(x1, recip(z0))))
   MARK(add(x0, first(x1, s(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(first(x1, s(z0))))
   MARK(add(x0, first(x1, 0))) -> c17(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0)))
   MARK(add(x0, first(x1, nil))) -> c17(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil)))
   MARK(add(x0, first(terms(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(first(terms(z0), x2)))
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   MARK(add(x0, first(dbl(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(first(dbl(z0), x2)))
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   MARK(add(dbl(z0), first(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
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   MARK(add(cons(z0, z1), first(x1, x2))) -> c17(MARK(first(x1, x2)))
   MARK(add(recip(z0), first(x1, x2))) -> c17(MARK(first(x1, x2)))
   MARK(add(s(z0), first(x1, x2))) -> c17(MARK(first(x1, x2)))
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   MARK(add(x0, cons(dbl(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(cons(dbl(z0), x2)))
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   MARK(add(x0, cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
   MARK(add(cons(z0, z1), cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
   MARK(add(recip(z0), cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
   MARK(add(s(z0), cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
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   MARK(add(x0, recip(sqr(z0)))) -> c17(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(recip(sqr(z0))))
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   MARK(add(0, recip(x1))) -> c17(A__ADD(0, recip(mark(x1))), MARK(recip(x1)))
   MARK(add(x0, recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(cons(z0, z1), recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(recip(z0), recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(s(z0), recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(nil, recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(terms(x0), s(z0))) -> c17(A__ADD(a__terms(mark(x0)), s(z0)), MARK(s(z0)))
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   MARK(add(terms(add(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(terms(dbl(z0)), x1)) -> c17(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(terms(first(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(terms(cons(z0, z1)), x1)) -> c17(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(x1))
   MARK(add(terms(recip(z0)), x1)) -> c17(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(terms(s(z0)), x1)) -> c17(A__ADD(a__terms(s(z0)), mark(x1)), MARK(x1))
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S tuples:
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   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
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   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
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   MARK(add(terms(nil), x1)) -> c17(A__ADD(a__terms(nil), mark(x1)), MARK(x1))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2


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

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

(162)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2))))
   MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0))
   MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0))
   MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0))
   MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0))
   MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1))))
   MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0))
   MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0))
   MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
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   MARK(add(x0, recip(first(z0, z1)))) -> c17(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(recip(first(z0, z1))))
   MARK(add(x0, recip(cons(z0, z1)))) -> c17(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(recip(cons(z0, z1))))
   MARK(add(x0, recip(recip(z0)))) -> c17(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(recip(recip(z0))))
   MARK(add(x0, recip(s(z0)))) -> c17(A__ADD(mark(x0), recip(s(z0))), MARK(recip(s(z0))))
   MARK(add(x0, recip(0))) -> c17(A__ADD(mark(x0), recip(0)), MARK(recip(0)))
   MARK(add(x0, recip(nil))) -> c17(A__ADD(mark(x0), recip(nil)), MARK(recip(nil)))
   MARK(add(terms(z0), recip(x1))) -> c17(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(sqr(z0), recip(x1))) -> c17(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(add(z0, z1), recip(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(dbl(z0), recip(x1))) -> c17(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(first(z0, z1), recip(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(0, recip(x1))) -> c17(A__ADD(0, recip(mark(x1))), MARK(recip(x1)))
   MARK(add(x0, recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(cons(z0, z1), recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(recip(z0), recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(s(z0), recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(nil, recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(terms(terms(z0)), x1)) -> c17(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(terms(sqr(z0)), x1)) -> c17(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(terms(add(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(terms(dbl(z0)), x1)) -> c17(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(terms(first(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(terms(cons(z0, z1)), x1)) -> c17(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(x1))
   MARK(add(terms(recip(z0)), x1)) -> c17(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(terms(s(z0)), x1)) -> c17(A__ADD(a__terms(s(z0)), mark(x1)), MARK(x1))
   MARK(add(terms(0), x1)) -> c17(A__ADD(a__terms(0), mark(x1)), MARK(x1))
   MARK(add(terms(nil), x1)) -> c17(A__ADD(a__terms(nil), mark(x1)), MARK(x1))
   MARK(add(terms(x0), s(z0))) -> c17(A__ADD(a__terms(mark(x0)), s(z0)))
   MARK(add(terms(x0), 0)) -> c17(A__ADD(a__terms(mark(x0)), 0))
   MARK(add(terms(x0), nil)) -> c17(A__ADD(a__terms(mark(x0)), nil))
   MARK(add(terms(x0), x1)) -> c17(MARK(x1))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2))))
   MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0))
   MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0))
   MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0))
   MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0))
   MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1))))
   MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0))
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   MARK(add(x0, cons(nil, x2))) -> c17(A__ADD(mark(x0), cons(nil, x2)), MARK(cons(nil, x2)))
   MARK(add(terms(z0), cons(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(sqr(z0), cons(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(add(z0, z1), cons(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(dbl(z0), cons(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(first(z0, z1), cons(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(0, cons(x1, x2))) -> c17(A__ADD(0, cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(x0, cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
   MARK(add(cons(z0, z1), cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
   MARK(add(recip(z0), cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
   MARK(add(s(z0), cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
   MARK(add(nil, cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
   MARK(add(x0, recip(terms(z0)))) -> c17(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(recip(terms(z0))))
   MARK(add(x0, recip(sqr(z0)))) -> c17(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(recip(sqr(z0))))
   MARK(add(x0, recip(add(z0, z1)))) -> c17(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(recip(add(z0, z1))))
   MARK(add(x0, recip(dbl(z0)))) -> c17(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(recip(dbl(z0))))
   MARK(add(x0, recip(first(z0, z1)))) -> c17(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(recip(first(z0, z1))))
   MARK(add(x0, recip(cons(z0, z1)))) -> c17(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(recip(cons(z0, z1))))
   MARK(add(x0, recip(recip(z0)))) -> c17(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(recip(recip(z0))))
   MARK(add(x0, recip(s(z0)))) -> c17(A__ADD(mark(x0), recip(s(z0))), MARK(recip(s(z0))))
   MARK(add(x0, recip(0))) -> c17(A__ADD(mark(x0), recip(0)), MARK(recip(0)))
   MARK(add(x0, recip(nil))) -> c17(A__ADD(mark(x0), recip(nil)), MARK(recip(nil)))
   MARK(add(terms(z0), recip(x1))) -> c17(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(sqr(z0), recip(x1))) -> c17(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(add(z0, z1), recip(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(dbl(z0), recip(x1))) -> c17(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(first(z0, z1), recip(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(0, recip(x1))) -> c17(A__ADD(0, recip(mark(x1))), MARK(recip(x1)))
   MARK(add(x0, recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(cons(z0, z1), recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(recip(z0), recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(s(z0), recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(nil, recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(terms(terms(z0)), x1)) -> c17(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(terms(sqr(z0)), x1)) -> c17(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(terms(add(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(terms(dbl(z0)), x1)) -> c17(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(terms(first(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(terms(cons(z0, z1)), x1)) -> c17(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(x1))
   MARK(add(terms(recip(z0)), x1)) -> c17(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(terms(s(z0)), x1)) -> c17(A__ADD(a__terms(s(z0)), mark(x1)), MARK(x1))
   MARK(add(terms(0), x1)) -> c17(A__ADD(a__terms(0), mark(x1)), MARK(x1))
   MARK(add(terms(nil), x1)) -> c17(A__ADD(a__terms(nil), mark(x1)), MARK(x1))
   MARK(add(terms(x0), s(z0))) -> c17(A__ADD(a__terms(mark(x0)), s(z0)))
   MARK(add(terms(x0), 0)) -> c17(A__ADD(a__terms(mark(x0)), 0))
   MARK(add(terms(x0), nil)) -> c17(A__ADD(a__terms(mark(x0)), nil))
   MARK(add(terms(x0), x1)) -> c17(MARK(x1))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2


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

(163) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) by 
   MARK(add(sqr(x0), terms(z0))) -> c17(A__ADD(a__sqr(mark(x0)), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(sqr(x0), sqr(z0))) -> c17(A__ADD(a__sqr(mark(x0)), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(sqr(x0), add(z0, z1))) -> c17(A__ADD(a__sqr(mark(x0)), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(sqr(x0), dbl(z0))) -> c17(A__ADD(a__sqr(mark(x0)), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(sqr(x0), first(z0, z1))) -> c17(A__ADD(a__sqr(mark(x0)), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(sqr(x0), cons(z0, z1))) -> c17(A__ADD(a__sqr(mark(x0)), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(sqr(x0), recip(z0))) -> c17(A__ADD(a__sqr(mark(x0)), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(sqr(x0), s(z0))) -> c17(A__ADD(a__sqr(mark(x0)), s(z0)), MARK(s(z0)))
   MARK(add(sqr(x0), 0)) -> c17(A__ADD(a__sqr(mark(x0)), 0), MARK(0))
   MARK(add(sqr(x0), nil)) -> c17(A__ADD(a__sqr(mark(x0)), nil), MARK(nil))
   MARK(add(sqr(x0), x1)) -> c17(A__ADD(sqr(mark(x0)), mark(x1)), MARK(x1))
   MARK(add(sqr(terms(z0)), x1)) -> c17(A__ADD(a__sqr(a__terms(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(sqr(sqr(z0)), x1)) -> c17(A__ADD(a__sqr(a__sqr(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(sqr(add(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(sqr(dbl(z0)), x1)) -> c17(A__ADD(a__sqr(a__dbl(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(sqr(first(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(sqr(cons(z0, z1)), x1)) -> c17(A__ADD(a__sqr(cons(mark(z0), z1)), mark(x1)), MARK(x1))
   MARK(add(sqr(recip(z0)), x1)) -> c17(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(sqr(s(z0)), x1)) -> c17(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(0), x1)) -> c17(A__ADD(a__sqr(0), mark(x1)), MARK(x1))
   MARK(add(sqr(nil), x1)) -> c17(A__ADD(a__sqr(nil), mark(x1)), MARK(x1))

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

(164)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
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   MARK(add(recip(z0), dbl(x1))) -> c17(MARK(dbl(x1)))
   MARK(add(s(z0), dbl(x1))) -> c17(MARK(dbl(x1)))
   MARK(add(nil, dbl(x1))) -> c17(MARK(dbl(x1)))
   MARK(add(x0, first(x1, x2))) -> c17(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(x0, first(x1, terms(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(first(x1, terms(z0))))
   MARK(add(x0, first(x1, sqr(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(first(x1, sqr(z0))))
   MARK(add(x0, first(x1, add(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(first(x1, add(z0, z1))))
   MARK(add(x0, first(x1, dbl(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(first(x1, dbl(z0))))
   MARK(add(x0, first(x1, first(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1))))
   MARK(add(x0, first(x1, cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1))))
   MARK(add(x0, first(x1, recip(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(first(x1, recip(z0))))
   MARK(add(x0, first(x1, s(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(first(x1, s(z0))))
   MARK(add(x0, first(x1, 0))) -> c17(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0)))
   MARK(add(x0, first(x1, nil))) -> c17(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil)))
   MARK(add(x0, first(terms(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(first(terms(z0), x2)))
   MARK(add(x0, first(sqr(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(first(sqr(z0), x2)))
   MARK(add(x0, first(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(first(add(z0, z1), x2)))
   MARK(add(x0, first(dbl(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(first(dbl(z0), x2)))
   MARK(add(x0, first(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2)))
   MARK(add(x0, first(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2)))
   MARK(add(x0, first(recip(z0), x2))) -> c17(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(first(recip(z0), x2)))
   MARK(add(x0, first(s(z0), x2))) -> c17(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(first(s(z0), x2)))
   MARK(add(x0, first(0, x2))) -> c17(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2)))
   MARK(add(x0, first(nil, x2))) -> c17(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2)))
   MARK(add(terms(z0), first(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(sqr(z0), first(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(add(z0, z1), first(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(dbl(z0), first(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(first(z0, z1), first(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(0, first(x1, x2))) -> c17(A__ADD(0, a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(cons(z0, z1), first(x1, x2))) -> c17(MARK(first(x1, x2)))
   MARK(add(recip(z0), first(x1, x2))) -> c17(MARK(first(x1, x2)))
   MARK(add(s(z0), first(x1, x2))) -> c17(MARK(first(x1, x2)))
   MARK(add(nil, first(x1, x2))) -> c17(MARK(first(x1, x2)))
   MARK(add(x0, cons(terms(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(cons(terms(z0), x2)))
   MARK(add(x0, cons(sqr(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(cons(sqr(z0), x2)))
   MARK(add(x0, cons(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(cons(add(z0, z1), x2)))
   MARK(add(x0, cons(dbl(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(cons(dbl(z0), x2)))
   MARK(add(x0, cons(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2)))
   MARK(add(x0, cons(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2)))
   MARK(add(x0, cons(recip(z0), x2))) -> c17(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(cons(recip(z0), x2)))
   MARK(add(x0, cons(s(z0), x2))) -> c17(A__ADD(mark(x0), cons(s(z0), x2)), MARK(cons(s(z0), x2)))
   MARK(add(x0, cons(0, x2))) -> c17(A__ADD(mark(x0), cons(0, x2)), MARK(cons(0, x2)))
   MARK(add(x0, cons(nil, x2))) -> c17(A__ADD(mark(x0), cons(nil, x2)), MARK(cons(nil, x2)))
   MARK(add(terms(z0), cons(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(sqr(z0), cons(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(add(z0, z1), cons(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(dbl(z0), cons(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(first(z0, z1), cons(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(0, cons(x1, x2))) -> c17(A__ADD(0, cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(x0, cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
   MARK(add(cons(z0, z1), cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
   MARK(add(recip(z0), cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
   MARK(add(s(z0), cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
   MARK(add(nil, cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
   MARK(add(x0, recip(terms(z0)))) -> c17(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(recip(terms(z0))))
   MARK(add(x0, recip(sqr(z0)))) -> c17(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(recip(sqr(z0))))
   MARK(add(x0, recip(add(z0, z1)))) -> c17(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(recip(add(z0, z1))))
   MARK(add(x0, recip(dbl(z0)))) -> c17(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(recip(dbl(z0))))
   MARK(add(x0, recip(first(z0, z1)))) -> c17(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(recip(first(z0, z1))))
   MARK(add(x0, recip(cons(z0, z1)))) -> c17(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(recip(cons(z0, z1))))
   MARK(add(x0, recip(recip(z0)))) -> c17(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(recip(recip(z0))))
   MARK(add(x0, recip(s(z0)))) -> c17(A__ADD(mark(x0), recip(s(z0))), MARK(recip(s(z0))))
   MARK(add(x0, recip(0))) -> c17(A__ADD(mark(x0), recip(0)), MARK(recip(0)))
   MARK(add(x0, recip(nil))) -> c17(A__ADD(mark(x0), recip(nil)), MARK(recip(nil)))
   MARK(add(terms(z0), recip(x1))) -> c17(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(sqr(z0), recip(x1))) -> c17(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(add(z0, z1), recip(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(dbl(z0), recip(x1))) -> c17(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(first(z0, z1), recip(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(0, recip(x1))) -> c17(A__ADD(0, recip(mark(x1))), MARK(recip(x1)))
   MARK(add(x0, recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(cons(z0, z1), recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(recip(z0), recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(s(z0), recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(nil, recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(terms(terms(z0)), x1)) -> c17(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(terms(sqr(z0)), x1)) -> c17(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(terms(add(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(terms(dbl(z0)), x1)) -> c17(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(terms(first(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(terms(cons(z0, z1)), x1)) -> c17(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(x1))
   MARK(add(terms(recip(z0)), x1)) -> c17(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(terms(s(z0)), x1)) -> c17(A__ADD(a__terms(s(z0)), mark(x1)), MARK(x1))
   MARK(add(terms(0), x1)) -> c17(A__ADD(a__terms(0), mark(x1)), MARK(x1))
   MARK(add(terms(nil), x1)) -> c17(A__ADD(a__terms(nil), mark(x1)), MARK(x1))
   MARK(add(terms(x0), s(z0))) -> c17(A__ADD(a__terms(mark(x0)), s(z0)))
   MARK(add(terms(x0), 0)) -> c17(A__ADD(a__terms(mark(x0)), 0))
   MARK(add(terms(x0), nil)) -> c17(A__ADD(a__terms(mark(x0)), nil))
   MARK(add(terms(x0), x1)) -> c17(MARK(x1))
   MARK(add(sqr(x0), s(z0))) -> c17(A__ADD(a__sqr(mark(x0)), s(z0)), MARK(s(z0)))
   MARK(add(sqr(x0), 0)) -> c17(A__ADD(a__sqr(mark(x0)), 0), MARK(0))
   MARK(add(sqr(x0), nil)) -> c17(A__ADD(a__sqr(mark(x0)), nil), MARK(nil))
   MARK(add(sqr(x0), x1)) -> c17(A__ADD(sqr(mark(x0)), mark(x1)), MARK(x1))
   MARK(add(sqr(terms(z0)), x1)) -> c17(A__ADD(a__sqr(a__terms(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(sqr(sqr(z0)), x1)) -> c17(A__ADD(a__sqr(a__sqr(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(sqr(add(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(sqr(dbl(z0)), x1)) -> c17(A__ADD(a__sqr(a__dbl(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(sqr(first(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(sqr(cons(z0, z1)), x1)) -> c17(A__ADD(a__sqr(cons(mark(z0), z1)), mark(x1)), MARK(x1))
   MARK(add(sqr(recip(z0)), x1)) -> c17(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(sqr(s(z0)), x1)) -> c17(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(0), x1)) -> c17(A__ADD(a__sqr(0), mark(x1)), MARK(x1))
   MARK(add(sqr(nil), x1)) -> c17(A__ADD(a__sqr(nil), mark(x1)), MARK(x1))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
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   MARK(add(first(z0, z1), add(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2)))
   MARK(add(0, add(x1, x2))) -> c17(A__ADD(0, a__add(mark(x1), mark(x2))), MARK(add(x1, x2)))
   MARK(add(cons(z0, z1), add(x1, x2))) -> c17(MARK(add(x1, x2)))
   MARK(add(recip(z0), add(x1, x2))) -> c17(MARK(add(x1, x2)))
   MARK(add(s(z0), add(x1, x2))) -> c17(MARK(add(x1, x2)))
   MARK(add(nil, add(x1, x2))) -> c17(MARK(add(x1, x2)))
   MARK(add(x0, dbl(x1))) -> c17(A__ADD(mark(x0), dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(x0, dbl(terms(z0)))) -> c17(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0))))
   MARK(add(x0, dbl(sqr(z0)))) -> c17(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0))))
   MARK(add(x0, dbl(add(z0, z1)))) -> c17(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1))))
   MARK(add(x0, dbl(dbl(z0)))) -> c17(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0))))
   MARK(add(x0, dbl(first(z0, z1)))) -> c17(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1))))
   MARK(add(x0, dbl(cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1))))
   MARK(add(x0, dbl(recip(z0)))) -> c17(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0))))
   MARK(add(x0, dbl(s(z0)))) -> c17(A__ADD(mark(x0), a__dbl(s(z0))), MARK(dbl(s(z0))))
   MARK(add(x0, dbl(0))) -> c17(A__ADD(mark(x0), a__dbl(0)), MARK(dbl(0)))
   MARK(add(x0, dbl(nil))) -> c17(A__ADD(mark(x0), a__dbl(nil)), MARK(dbl(nil)))
   MARK(add(terms(z0), dbl(x1))) -> c17(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(sqr(z0), dbl(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(add(z0, z1), dbl(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(dbl(z0), dbl(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(first(z0, z1), dbl(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(0, dbl(x1))) -> c17(A__ADD(0, a__dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(x0, dbl(x1))) -> c17(MARK(dbl(x1)))
   MARK(add(cons(z0, z1), dbl(x1))) -> c17(MARK(dbl(x1)))
   MARK(add(recip(z0), dbl(x1))) -> c17(MARK(dbl(x1)))
   MARK(add(s(z0), dbl(x1))) -> c17(MARK(dbl(x1)))
   MARK(add(nil, dbl(x1))) -> c17(MARK(dbl(x1)))
   MARK(add(x0, first(x1, x2))) -> c17(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(x0, first(x1, terms(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(first(x1, terms(z0))))
   MARK(add(x0, first(x1, sqr(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(first(x1, sqr(z0))))
   MARK(add(x0, first(x1, add(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(first(x1, add(z0, z1))))
   MARK(add(x0, first(x1, dbl(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(first(x1, dbl(z0))))
   MARK(add(x0, first(x1, first(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1))))
   MARK(add(x0, first(x1, cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1))))
   MARK(add(x0, first(x1, recip(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(first(x1, recip(z0))))
   MARK(add(x0, first(x1, s(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(first(x1, s(z0))))
   MARK(add(x0, first(x1, 0))) -> c17(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0)))
   MARK(add(x0, first(x1, nil))) -> c17(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil)))
   MARK(add(x0, first(terms(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(first(terms(z0), x2)))
   MARK(add(x0, first(sqr(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(first(sqr(z0), x2)))
   MARK(add(x0, first(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(first(add(z0, z1), x2)))
   MARK(add(x0, first(dbl(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(first(dbl(z0), x2)))
   MARK(add(x0, first(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2)))
   MARK(add(x0, first(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2)))
   MARK(add(x0, first(recip(z0), x2))) -> c17(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(first(recip(z0), x2)))
   MARK(add(x0, first(s(z0), x2))) -> c17(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(first(s(z0), x2)))
   MARK(add(x0, first(0, x2))) -> c17(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2)))
   MARK(add(x0, first(nil, x2))) -> c17(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2)))
   MARK(add(terms(z0), first(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(sqr(z0), first(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(add(z0, z1), first(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(dbl(z0), first(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(first(z0, z1), first(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(0, first(x1, x2))) -> c17(A__ADD(0, a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(cons(z0, z1), first(x1, x2))) -> c17(MARK(first(x1, x2)))
   MARK(add(recip(z0), first(x1, x2))) -> c17(MARK(first(x1, x2)))
   MARK(add(s(z0), first(x1, x2))) -> c17(MARK(first(x1, x2)))
   MARK(add(nil, first(x1, x2))) -> c17(MARK(first(x1, x2)))
   MARK(add(x0, cons(terms(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(cons(terms(z0), x2)))
   MARK(add(x0, cons(sqr(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(cons(sqr(z0), x2)))
   MARK(add(x0, cons(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(cons(add(z0, z1), x2)))
   MARK(add(x0, cons(dbl(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(cons(dbl(z0), x2)))
   MARK(add(x0, cons(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2)))
   MARK(add(x0, cons(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2)))
   MARK(add(x0, cons(recip(z0), x2))) -> c17(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(cons(recip(z0), x2)))
   MARK(add(x0, cons(s(z0), x2))) -> c17(A__ADD(mark(x0), cons(s(z0), x2)), MARK(cons(s(z0), x2)))
   MARK(add(x0, cons(0, x2))) -> c17(A__ADD(mark(x0), cons(0, x2)), MARK(cons(0, x2)))
   MARK(add(x0, cons(nil, x2))) -> c17(A__ADD(mark(x0), cons(nil, x2)), MARK(cons(nil, x2)))
   MARK(add(terms(z0), cons(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(sqr(z0), cons(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(add(z0, z1), cons(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(dbl(z0), cons(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(first(z0, z1), cons(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(0, cons(x1, x2))) -> c17(A__ADD(0, cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(x0, cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
   MARK(add(cons(z0, z1), cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
   MARK(add(recip(z0), cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
   MARK(add(s(z0), cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
   MARK(add(nil, cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
   MARK(add(x0, recip(terms(z0)))) -> c17(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(recip(terms(z0))))
   MARK(add(x0, recip(sqr(z0)))) -> c17(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(recip(sqr(z0))))
   MARK(add(x0, recip(add(z0, z1)))) -> c17(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(recip(add(z0, z1))))
   MARK(add(x0, recip(dbl(z0)))) -> c17(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(recip(dbl(z0))))
   MARK(add(x0, recip(first(z0, z1)))) -> c17(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(recip(first(z0, z1))))
   MARK(add(x0, recip(cons(z0, z1)))) -> c17(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(recip(cons(z0, z1))))
   MARK(add(x0, recip(recip(z0)))) -> c17(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(recip(recip(z0))))
   MARK(add(x0, recip(s(z0)))) -> c17(A__ADD(mark(x0), recip(s(z0))), MARK(recip(s(z0))))
   MARK(add(x0, recip(0))) -> c17(A__ADD(mark(x0), recip(0)), MARK(recip(0)))
   MARK(add(x0, recip(nil))) -> c17(A__ADD(mark(x0), recip(nil)), MARK(recip(nil)))
   MARK(add(terms(z0), recip(x1))) -> c17(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(sqr(z0), recip(x1))) -> c17(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(add(z0, z1), recip(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(dbl(z0), recip(x1))) -> c17(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(first(z0, z1), recip(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(0, recip(x1))) -> c17(A__ADD(0, recip(mark(x1))), MARK(recip(x1)))
   MARK(add(x0, recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(cons(z0, z1), recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(recip(z0), recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(s(z0), recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(nil, recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(terms(terms(z0)), x1)) -> c17(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(terms(sqr(z0)), x1)) -> c17(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(terms(add(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(terms(dbl(z0)), x1)) -> c17(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(terms(first(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(terms(cons(z0, z1)), x1)) -> c17(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(x1))
   MARK(add(terms(recip(z0)), x1)) -> c17(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(terms(s(z0)), x1)) -> c17(A__ADD(a__terms(s(z0)), mark(x1)), MARK(x1))
   MARK(add(terms(0), x1)) -> c17(A__ADD(a__terms(0), mark(x1)), MARK(x1))
   MARK(add(terms(nil), x1)) -> c17(A__ADD(a__terms(nil), mark(x1)), MARK(x1))
   MARK(add(terms(x0), s(z0))) -> c17(A__ADD(a__terms(mark(x0)), s(z0)))
   MARK(add(terms(x0), 0)) -> c17(A__ADD(a__terms(mark(x0)), 0))
   MARK(add(terms(x0), nil)) -> c17(A__ADD(a__terms(mark(x0)), nil))
   MARK(add(terms(x0), x1)) -> c17(MARK(x1))
   MARK(add(sqr(x0), s(z0))) -> c17(A__ADD(a__sqr(mark(x0)), s(z0)), MARK(s(z0)))
   MARK(add(sqr(x0), 0)) -> c17(A__ADD(a__sqr(mark(x0)), 0), MARK(0))
   MARK(add(sqr(x0), nil)) -> c17(A__ADD(a__sqr(mark(x0)), nil), MARK(nil))
   MARK(add(sqr(x0), x1)) -> c17(A__ADD(sqr(mark(x0)), mark(x1)), MARK(x1))
   MARK(add(sqr(terms(z0)), x1)) -> c17(A__ADD(a__sqr(a__terms(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(sqr(sqr(z0)), x1)) -> c17(A__ADD(a__sqr(a__sqr(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(sqr(add(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(sqr(dbl(z0)), x1)) -> c17(A__ADD(a__sqr(a__dbl(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(sqr(first(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(sqr(cons(z0, z1)), x1)) -> c17(A__ADD(a__sqr(cons(mark(z0), z1)), mark(x1)), MARK(x1))
   MARK(add(sqr(recip(z0)), x1)) -> c17(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(sqr(s(z0)), x1)) -> c17(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(0), x1)) -> c17(A__ADD(a__sqr(0), mark(x1)), MARK(x1))
   MARK(add(sqr(nil), x1)) -> c17(A__ADD(a__sqr(nil), mark(x1)), MARK(x1))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2


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

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

(166)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
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   MARK(add(sqr(dbl(z0)), x1)) -> c17(A__ADD(a__sqr(a__dbl(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(sqr(first(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(sqr(cons(z0, z1)), x1)) -> c17(A__ADD(a__sqr(cons(mark(z0), z1)), mark(x1)), MARK(x1))
   MARK(add(sqr(recip(z0)), x1)) -> c17(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(sqr(s(z0)), x1)) -> c17(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(0), x1)) -> c17(A__ADD(a__sqr(0), mark(x1)), MARK(x1))
   MARK(add(sqr(nil), x1)) -> c17(A__ADD(a__sqr(nil), mark(x1)), MARK(x1))
   MARK(add(sqr(x0), s(z0))) -> c17(A__ADD(a__sqr(mark(x0)), s(z0)))
   MARK(add(sqr(x0), 0)) -> c17(A__ADD(a__sqr(mark(x0)), 0))
   MARK(add(sqr(x0), nil)) -> c17(A__ADD(a__sqr(mark(x0)), nil))
   MARK(add(sqr(x0), x1)) -> c17(MARK(x1))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2))))
   MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0))
   MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0))
   MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0))
   MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0))
   MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1))))
   MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0))
   MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0))
   MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0))
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   MARK(add(x0, recip(recip(z0)))) -> c17(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(recip(recip(z0))))
   MARK(add(x0, recip(s(z0)))) -> c17(A__ADD(mark(x0), recip(s(z0))), MARK(recip(s(z0))))
   MARK(add(x0, recip(0))) -> c17(A__ADD(mark(x0), recip(0)), MARK(recip(0)))
   MARK(add(x0, recip(nil))) -> c17(A__ADD(mark(x0), recip(nil)), MARK(recip(nil)))
   MARK(add(terms(z0), recip(x1))) -> c17(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(sqr(z0), recip(x1))) -> c17(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(add(z0, z1), recip(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(dbl(z0), recip(x1))) -> c17(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(first(z0, z1), recip(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(0, recip(x1))) -> c17(A__ADD(0, recip(mark(x1))), MARK(recip(x1)))
   MARK(add(x0, recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(cons(z0, z1), recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(recip(z0), recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(s(z0), recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(nil, recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(terms(terms(z0)), x1)) -> c17(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(terms(sqr(z0)), x1)) -> c17(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(terms(add(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(terms(dbl(z0)), x1)) -> c17(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(terms(first(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(terms(cons(z0, z1)), x1)) -> c17(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(x1))
   MARK(add(terms(recip(z0)), x1)) -> c17(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(terms(s(z0)), x1)) -> c17(A__ADD(a__terms(s(z0)), mark(x1)), MARK(x1))
   MARK(add(terms(0), x1)) -> c17(A__ADD(a__terms(0), mark(x1)), MARK(x1))
   MARK(add(terms(nil), x1)) -> c17(A__ADD(a__terms(nil), mark(x1)), MARK(x1))
   MARK(add(terms(x0), s(z0))) -> c17(A__ADD(a__terms(mark(x0)), s(z0)))
   MARK(add(terms(x0), 0)) -> c17(A__ADD(a__terms(mark(x0)), 0))
   MARK(add(terms(x0), nil)) -> c17(A__ADD(a__terms(mark(x0)), nil))
   MARK(add(terms(x0), x1)) -> c17(MARK(x1))
   MARK(add(sqr(terms(z0)), x1)) -> c17(A__ADD(a__sqr(a__terms(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(sqr(sqr(z0)), x1)) -> c17(A__ADD(a__sqr(a__sqr(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(sqr(add(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(sqr(dbl(z0)), x1)) -> c17(A__ADD(a__sqr(a__dbl(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(sqr(first(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(sqr(cons(z0, z1)), x1)) -> c17(A__ADD(a__sqr(cons(mark(z0), z1)), mark(x1)), MARK(x1))
   MARK(add(sqr(recip(z0)), x1)) -> c17(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(sqr(s(z0)), x1)) -> c17(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(0), x1)) -> c17(A__ADD(a__sqr(0), mark(x1)), MARK(x1))
   MARK(add(sqr(nil), x1)) -> c17(A__ADD(a__sqr(nil), mark(x1)), MARK(x1))
   MARK(add(sqr(x0), s(z0))) -> c17(A__ADD(a__sqr(mark(x0)), s(z0)))
   MARK(add(sqr(x0), 0)) -> c17(A__ADD(a__sqr(mark(x0)), 0))
   MARK(add(sqr(x0), nil)) -> c17(A__ADD(a__sqr(mark(x0)), nil))
   MARK(add(sqr(x0), x1)) -> c17(MARK(x1))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2


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

(167) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) by 
   MARK(add(add(x0, x1), terms(z0))) -> c17(A__ADD(a__add(mark(x0), mark(x1)), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(add(x0, x1), sqr(z0))) -> c17(A__ADD(a__add(mark(x0), mark(x1)), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(add(x0, x1), add(z0, z1))) -> c17(A__ADD(a__add(mark(x0), mark(x1)), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(add(x0, x1), dbl(z0))) -> c17(A__ADD(a__add(mark(x0), mark(x1)), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(add(x0, x1), first(z0, z1))) -> c17(A__ADD(a__add(mark(x0), mark(x1)), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(add(x0, x1), cons(z0, z1))) -> c17(A__ADD(a__add(mark(x0), mark(x1)), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(add(x0, x1), recip(z0))) -> c17(A__ADD(a__add(mark(x0), mark(x1)), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(add(x0, x1), s(z0))) -> c17(A__ADD(a__add(mark(x0), mark(x1)), s(z0)), MARK(s(z0)))
   MARK(add(add(x0, x1), 0)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), 0), MARK(0))
   MARK(add(add(x0, x1), nil)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), nil), MARK(nil))
   MARK(add(add(x0, x1), x2)) -> c17(A__ADD(add(mark(x0), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(x0, terms(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(add(x0, sqr(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(add(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   MARK(add(add(x0, dbl(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(add(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   MARK(add(add(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2))
   MARK(add(add(x0, recip(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(add(x0, s(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), s(z0)), mark(x2)), MARK(x2))
   MARK(add(add(x0, 0), x2)) -> c17(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(x2))
   MARK(add(add(x0, nil), x2)) -> c17(A__ADD(a__add(mark(x0), nil), mark(x2)), MARK(x2))
   MARK(add(add(terms(z0), x1), x2)) -> c17(A__ADD(a__add(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(sqr(z0), x1), x2)) -> c17(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(add(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(dbl(z0), x1), x2)) -> c17(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(first(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(recip(z0), x1), x2)) -> c17(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(s(z0), x1), x2)) -> c17(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(0, x1), x2)) -> c17(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(nil, x1), x2)) -> c17(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(x2))

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

(168)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
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   MARK(add(add(z0, z1), dbl(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(dbl(z0), dbl(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(first(z0, z1), dbl(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(0, dbl(x1))) -> c17(A__ADD(0, a__dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(x0, dbl(x1))) -> c17(MARK(dbl(x1)))
   MARK(add(cons(z0, z1), dbl(x1))) -> c17(MARK(dbl(x1)))
   MARK(add(recip(z0), dbl(x1))) -> c17(MARK(dbl(x1)))
   MARK(add(s(z0), dbl(x1))) -> c17(MARK(dbl(x1)))
   MARK(add(nil, dbl(x1))) -> c17(MARK(dbl(x1)))
   MARK(add(x0, first(x1, x2))) -> c17(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(x0, first(x1, terms(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(first(x1, terms(z0))))
   MARK(add(x0, first(x1, sqr(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(first(x1, sqr(z0))))
   MARK(add(x0, first(x1, add(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(first(x1, add(z0, z1))))
   MARK(add(x0, first(x1, dbl(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(first(x1, dbl(z0))))
   MARK(add(x0, first(x1, first(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1))))
   MARK(add(x0, first(x1, cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1))))
   MARK(add(x0, first(x1, recip(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(first(x1, recip(z0))))
   MARK(add(x0, first(x1, s(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(first(x1, s(z0))))
   MARK(add(x0, first(x1, 0))) -> c17(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0)))
   MARK(add(x0, first(x1, nil))) -> c17(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil)))
   MARK(add(x0, first(terms(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(first(terms(z0), x2)))
   MARK(add(x0, first(sqr(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(first(sqr(z0), x2)))
   MARK(add(x0, first(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(first(add(z0, z1), x2)))
   MARK(add(x0, first(dbl(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(first(dbl(z0), x2)))
   MARK(add(x0, first(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2)))
   MARK(add(x0, first(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2)))
   MARK(add(x0, first(recip(z0), x2))) -> c17(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(first(recip(z0), x2)))
   MARK(add(x0, first(s(z0), x2))) -> c17(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(first(s(z0), x2)))
   MARK(add(x0, first(0, x2))) -> c17(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2)))
   MARK(add(x0, first(nil, x2))) -> c17(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2)))
   MARK(add(terms(z0), first(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(sqr(z0), first(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
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   MARK(add(dbl(z0), first(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(first(z0, z1), first(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(0, first(x1, x2))) -> c17(A__ADD(0, a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(cons(z0, z1), first(x1, x2))) -> c17(MARK(first(x1, x2)))
   MARK(add(recip(z0), first(x1, x2))) -> c17(MARK(first(x1, x2)))
   MARK(add(s(z0), first(x1, x2))) -> c17(MARK(first(x1, x2)))
   MARK(add(nil, first(x1, x2))) -> c17(MARK(first(x1, x2)))
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   MARK(add(x0, cons(sqr(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(cons(sqr(z0), x2)))
   MARK(add(x0, cons(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(cons(add(z0, z1), x2)))
   MARK(add(x0, cons(dbl(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(cons(dbl(z0), x2)))
   MARK(add(x0, cons(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2)))
   MARK(add(x0, cons(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2)))
   MARK(add(x0, cons(recip(z0), x2))) -> c17(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(cons(recip(z0), x2)))
   MARK(add(x0, cons(s(z0), x2))) -> c17(A__ADD(mark(x0), cons(s(z0), x2)), MARK(cons(s(z0), x2)))
   MARK(add(x0, cons(0, x2))) -> c17(A__ADD(mark(x0), cons(0, x2)), MARK(cons(0, x2)))
   MARK(add(x0, cons(nil, x2))) -> c17(A__ADD(mark(x0), cons(nil, x2)), MARK(cons(nil, x2)))
   MARK(add(terms(z0), cons(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(sqr(z0), cons(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(add(z0, z1), cons(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(dbl(z0), cons(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(first(z0, z1), cons(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(0, cons(x1, x2))) -> c17(A__ADD(0, cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(x0, cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
   MARK(add(cons(z0, z1), cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
   MARK(add(recip(z0), cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
   MARK(add(s(z0), cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
   MARK(add(nil, cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
   MARK(add(x0, recip(terms(z0)))) -> c17(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(recip(terms(z0))))
   MARK(add(x0, recip(sqr(z0)))) -> c17(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(recip(sqr(z0))))
   MARK(add(x0, recip(add(z0, z1)))) -> c17(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(recip(add(z0, z1))))
   MARK(add(x0, recip(dbl(z0)))) -> c17(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(recip(dbl(z0))))
   MARK(add(x0, recip(first(z0, z1)))) -> c17(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(recip(first(z0, z1))))
   MARK(add(x0, recip(cons(z0, z1)))) -> c17(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(recip(cons(z0, z1))))
   MARK(add(x0, recip(recip(z0)))) -> c17(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(recip(recip(z0))))
   MARK(add(x0, recip(s(z0)))) -> c17(A__ADD(mark(x0), recip(s(z0))), MARK(recip(s(z0))))
   MARK(add(x0, recip(0))) -> c17(A__ADD(mark(x0), recip(0)), MARK(recip(0)))
   MARK(add(x0, recip(nil))) -> c17(A__ADD(mark(x0), recip(nil)), MARK(recip(nil)))
   MARK(add(terms(z0), recip(x1))) -> c17(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(sqr(z0), recip(x1))) -> c17(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(add(z0, z1), recip(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(dbl(z0), recip(x1))) -> c17(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(first(z0, z1), recip(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(0, recip(x1))) -> c17(A__ADD(0, recip(mark(x1))), MARK(recip(x1)))
   MARK(add(x0, recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(cons(z0, z1), recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(recip(z0), recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(s(z0), recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(nil, recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(terms(terms(z0)), x1)) -> c17(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(terms(sqr(z0)), x1)) -> c17(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(terms(add(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(terms(dbl(z0)), x1)) -> c17(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(terms(first(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(terms(cons(z0, z1)), x1)) -> c17(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(x1))
   MARK(add(terms(recip(z0)), x1)) -> c17(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(terms(s(z0)), x1)) -> c17(A__ADD(a__terms(s(z0)), mark(x1)), MARK(x1))
   MARK(add(terms(0), x1)) -> c17(A__ADD(a__terms(0), mark(x1)), MARK(x1))
   MARK(add(terms(nil), x1)) -> c17(A__ADD(a__terms(nil), mark(x1)), MARK(x1))
   MARK(add(terms(x0), s(z0))) -> c17(A__ADD(a__terms(mark(x0)), s(z0)))
   MARK(add(terms(x0), 0)) -> c17(A__ADD(a__terms(mark(x0)), 0))
   MARK(add(terms(x0), nil)) -> c17(A__ADD(a__terms(mark(x0)), nil))
   MARK(add(terms(x0), x1)) -> c17(MARK(x1))
   MARK(add(sqr(terms(z0)), x1)) -> c17(A__ADD(a__sqr(a__terms(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(sqr(sqr(z0)), x1)) -> c17(A__ADD(a__sqr(a__sqr(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(sqr(add(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(sqr(dbl(z0)), x1)) -> c17(A__ADD(a__sqr(a__dbl(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(sqr(first(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(sqr(cons(z0, z1)), x1)) -> c17(A__ADD(a__sqr(cons(mark(z0), z1)), mark(x1)), MARK(x1))
   MARK(add(sqr(recip(z0)), x1)) -> c17(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(sqr(s(z0)), x1)) -> c17(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(0), x1)) -> c17(A__ADD(a__sqr(0), mark(x1)), MARK(x1))
   MARK(add(sqr(nil), x1)) -> c17(A__ADD(a__sqr(nil), mark(x1)), MARK(x1))
   MARK(add(sqr(x0), s(z0))) -> c17(A__ADD(a__sqr(mark(x0)), s(z0)))
   MARK(add(sqr(x0), 0)) -> c17(A__ADD(a__sqr(mark(x0)), 0))
   MARK(add(sqr(x0), nil)) -> c17(A__ADD(a__sqr(mark(x0)), nil))
   MARK(add(sqr(x0), x1)) -> c17(MARK(x1))
   MARK(add(add(x0, x1), s(z0))) -> c17(A__ADD(a__add(mark(x0), mark(x1)), s(z0)), MARK(s(z0)))
   MARK(add(add(x0, x1), 0)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), 0), MARK(0))
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   MARK(add(add(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   MARK(add(add(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2))
   MARK(add(add(x0, recip(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(add(x0, s(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), s(z0)), mark(x2)), MARK(x2))
   MARK(add(add(x0, 0), x2)) -> c17(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(x2))
   MARK(add(add(x0, nil), x2)) -> c17(A__ADD(a__add(mark(x0), nil), mark(x2)), MARK(x2))
   MARK(add(add(terms(z0), x1), x2)) -> c17(A__ADD(a__add(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(sqr(z0), x1), x2)) -> c17(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(add(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(dbl(z0), x1), x2)) -> c17(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(first(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(recip(z0), x1), x2)) -> c17(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(s(z0), x1), x2)) -> c17(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(0, x1), x2)) -> c17(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(nil, x1), x2)) -> c17(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(x2))
S tuples:
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   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
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   MARK(add(add(x0, x1), s(z0))) -> c17(A__ADD(a__add(mark(x0), mark(x1)), s(z0)), MARK(s(z0)))
   MARK(add(add(x0, x1), 0)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), 0), MARK(0))
   MARK(add(add(x0, x1), nil)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), nil), MARK(nil))
   MARK(add(add(x0, x1), x2)) -> c17(A__ADD(add(mark(x0), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(x0, terms(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(add(x0, sqr(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(add(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   MARK(add(add(x0, dbl(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(add(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   MARK(add(add(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2))
   MARK(add(add(x0, recip(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(add(x0, s(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), s(z0)), mark(x2)), MARK(x2))
   MARK(add(add(x0, 0), x2)) -> c17(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(x2))
   MARK(add(add(x0, nil), x2)) -> c17(A__ADD(a__add(mark(x0), nil), mark(x2)), MARK(x2))
   MARK(add(add(terms(z0), x1), x2)) -> c17(A__ADD(a__add(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(sqr(z0), x1), x2)) -> c17(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(add(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(dbl(z0), x1), x2)) -> c17(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(first(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(recip(z0), x1), x2)) -> c17(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(s(z0), x1), x2)) -> c17(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(0, x1), x2)) -> c17(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(nil, x1), x2)) -> c17(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(x2))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2


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

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

(170)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2))))
   MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0))
   MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0))
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   MARK(add(x0, cons(sqr(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(cons(sqr(z0), x2)))
   MARK(add(x0, cons(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(cons(add(z0, z1), x2)))
   MARK(add(x0, cons(dbl(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(cons(dbl(z0), x2)))
   MARK(add(x0, cons(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2)))
   MARK(add(x0, cons(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2)))
   MARK(add(x0, cons(recip(z0), x2))) -> c17(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(cons(recip(z0), x2)))
   MARK(add(x0, cons(s(z0), x2))) -> c17(A__ADD(mark(x0), cons(s(z0), x2)), MARK(cons(s(z0), x2)))
   MARK(add(x0, cons(0, x2))) -> c17(A__ADD(mark(x0), cons(0, x2)), MARK(cons(0, x2)))
   MARK(add(x0, cons(nil, x2))) -> c17(A__ADD(mark(x0), cons(nil, x2)), MARK(cons(nil, x2)))
   MARK(add(terms(z0), cons(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(sqr(z0), cons(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(add(z0, z1), cons(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(dbl(z0), cons(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(first(z0, z1), cons(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(0, cons(x1, x2))) -> c17(A__ADD(0, cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(x0, cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
   MARK(add(cons(z0, z1), cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
   MARK(add(recip(z0), cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
   MARK(add(s(z0), cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
   MARK(add(nil, cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
   MARK(add(x0, recip(terms(z0)))) -> c17(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(recip(terms(z0))))
   MARK(add(x0, recip(sqr(z0)))) -> c17(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(recip(sqr(z0))))
   MARK(add(x0, recip(add(z0, z1)))) -> c17(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(recip(add(z0, z1))))
   MARK(add(x0, recip(dbl(z0)))) -> c17(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(recip(dbl(z0))))
   MARK(add(x0, recip(first(z0, z1)))) -> c17(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(recip(first(z0, z1))))
   MARK(add(x0, recip(cons(z0, z1)))) -> c17(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(recip(cons(z0, z1))))
   MARK(add(x0, recip(recip(z0)))) -> c17(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(recip(recip(z0))))
   MARK(add(x0, recip(s(z0)))) -> c17(A__ADD(mark(x0), recip(s(z0))), MARK(recip(s(z0))))
   MARK(add(x0, recip(0))) -> c17(A__ADD(mark(x0), recip(0)), MARK(recip(0)))
   MARK(add(x0, recip(nil))) -> c17(A__ADD(mark(x0), recip(nil)), MARK(recip(nil)))
   MARK(add(terms(z0), recip(x1))) -> c17(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(sqr(z0), recip(x1))) -> c17(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(add(z0, z1), recip(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(dbl(z0), recip(x1))) -> c17(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(first(z0, z1), recip(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(0, recip(x1))) -> c17(A__ADD(0, recip(mark(x1))), MARK(recip(x1)))
   MARK(add(x0, recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(cons(z0, z1), recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(recip(z0), recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(s(z0), recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(nil, recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(terms(terms(z0)), x1)) -> c17(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(terms(sqr(z0)), x1)) -> c17(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(terms(add(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(terms(dbl(z0)), x1)) -> c17(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(terms(first(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(terms(cons(z0, z1)), x1)) -> c17(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(x1))
   MARK(add(terms(recip(z0)), x1)) -> c17(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(terms(s(z0)), x1)) -> c17(A__ADD(a__terms(s(z0)), mark(x1)), MARK(x1))
   MARK(add(terms(0), x1)) -> c17(A__ADD(a__terms(0), mark(x1)), MARK(x1))
   MARK(add(terms(nil), x1)) -> c17(A__ADD(a__terms(nil), mark(x1)), MARK(x1))
   MARK(add(terms(x0), s(z0))) -> c17(A__ADD(a__terms(mark(x0)), s(z0)))
   MARK(add(terms(x0), 0)) -> c17(A__ADD(a__terms(mark(x0)), 0))
   MARK(add(terms(x0), nil)) -> c17(A__ADD(a__terms(mark(x0)), nil))
   MARK(add(terms(x0), x1)) -> c17(MARK(x1))
   MARK(add(sqr(terms(z0)), x1)) -> c17(A__ADD(a__sqr(a__terms(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(sqr(sqr(z0)), x1)) -> c17(A__ADD(a__sqr(a__sqr(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(sqr(add(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(sqr(dbl(z0)), x1)) -> c17(A__ADD(a__sqr(a__dbl(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(sqr(first(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(sqr(cons(z0, z1)), x1)) -> c17(A__ADD(a__sqr(cons(mark(z0), z1)), mark(x1)), MARK(x1))
   MARK(add(sqr(recip(z0)), x1)) -> c17(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(sqr(s(z0)), x1)) -> c17(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(0), x1)) -> c17(A__ADD(a__sqr(0), mark(x1)), MARK(x1))
   MARK(add(sqr(nil), x1)) -> c17(A__ADD(a__sqr(nil), mark(x1)), MARK(x1))
   MARK(add(sqr(x0), s(z0))) -> c17(A__ADD(a__sqr(mark(x0)), s(z0)))
   MARK(add(sqr(x0), 0)) -> c17(A__ADD(a__sqr(mark(x0)), 0))
   MARK(add(sqr(x0), nil)) -> c17(A__ADD(a__sqr(mark(x0)), nil))
   MARK(add(sqr(x0), x1)) -> c17(MARK(x1))
   MARK(add(add(x0, terms(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(add(x0, sqr(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(add(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   MARK(add(add(x0, dbl(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(add(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   MARK(add(add(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2))
   MARK(add(add(x0, recip(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(add(x0, s(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), s(z0)), mark(x2)), MARK(x2))
   MARK(add(add(x0, 0), x2)) -> c17(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(x2))
   MARK(add(add(x0, nil), x2)) -> c17(A__ADD(a__add(mark(x0), nil), mark(x2)), MARK(x2))
   MARK(add(add(terms(z0), x1), x2)) -> c17(A__ADD(a__add(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(sqr(z0), x1), x2)) -> c17(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(add(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(dbl(z0), x1), x2)) -> c17(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(first(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(recip(z0), x1), x2)) -> c17(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(s(z0), x1), x2)) -> c17(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(0, x1), x2)) -> c17(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(nil, x1), x2)) -> c17(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(x0, x1), s(z0))) -> c17(A__ADD(a__add(mark(x0), mark(x1)), s(z0)))
   MARK(add(add(x0, x1), 0)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), 0))
   MARK(add(add(x0, x1), nil)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), nil))
   MARK(add(add(x0, x1), x2)) -> c17(MARK(x2))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
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   MARK(add(x0, dbl(0))) -> c17(A__ADD(mark(x0), a__dbl(0)), MARK(dbl(0)))
   MARK(add(x0, dbl(nil))) -> c17(A__ADD(mark(x0), a__dbl(nil)), MARK(dbl(nil)))
   MARK(add(terms(z0), dbl(x1))) -> c17(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(sqr(z0), dbl(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(add(z0, z1), dbl(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(dbl(z0), dbl(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(first(z0, z1), dbl(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(0, dbl(x1))) -> c17(A__ADD(0, a__dbl(mark(x1))), MARK(dbl(x1)))
   MARK(add(x0, dbl(x1))) -> c17(MARK(dbl(x1)))
   MARK(add(cons(z0, z1), dbl(x1))) -> c17(MARK(dbl(x1)))
   MARK(add(recip(z0), dbl(x1))) -> c17(MARK(dbl(x1)))
   MARK(add(s(z0), dbl(x1))) -> c17(MARK(dbl(x1)))
   MARK(add(nil, dbl(x1))) -> c17(MARK(dbl(x1)))
   MARK(add(x0, first(x1, x2))) -> c17(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(x0, first(x1, terms(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(first(x1, terms(z0))))
   MARK(add(x0, first(x1, sqr(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(first(x1, sqr(z0))))
   MARK(add(x0, first(x1, add(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(first(x1, add(z0, z1))))
   MARK(add(x0, first(x1, dbl(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(first(x1, dbl(z0))))
   MARK(add(x0, first(x1, first(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1))))
   MARK(add(x0, first(x1, cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1))))
   MARK(add(x0, first(x1, recip(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(first(x1, recip(z0))))
   MARK(add(x0, first(x1, s(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(first(x1, s(z0))))
   MARK(add(x0, first(x1, 0))) -> c17(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0)))
   MARK(add(x0, first(x1, nil))) -> c17(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil)))
   MARK(add(x0, first(terms(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(first(terms(z0), x2)))
   MARK(add(x0, first(sqr(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(first(sqr(z0), x2)))
   MARK(add(x0, first(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(first(add(z0, z1), x2)))
   MARK(add(x0, first(dbl(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(first(dbl(z0), x2)))
   MARK(add(x0, first(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2)))
   MARK(add(x0, first(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2)))
   MARK(add(x0, first(recip(z0), x2))) -> c17(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(first(recip(z0), x2)))
   MARK(add(x0, first(s(z0), x2))) -> c17(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(first(s(z0), x2)))
   MARK(add(x0, first(0, x2))) -> c17(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2)))
   MARK(add(x0, first(nil, x2))) -> c17(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2)))
   MARK(add(terms(z0), first(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(sqr(z0), first(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(add(z0, z1), first(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(dbl(z0), first(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(first(z0, z1), first(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(0, first(x1, x2))) -> c17(A__ADD(0, a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(cons(z0, z1), first(x1, x2))) -> c17(MARK(first(x1, x2)))
   MARK(add(recip(z0), first(x1, x2))) -> c17(MARK(first(x1, x2)))
   MARK(add(s(z0), first(x1, x2))) -> c17(MARK(first(x1, x2)))
   MARK(add(nil, first(x1, x2))) -> c17(MARK(first(x1, x2)))
   MARK(add(x0, cons(terms(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(cons(terms(z0), x2)))
   MARK(add(x0, cons(sqr(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(cons(sqr(z0), x2)))
   MARK(add(x0, cons(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(cons(add(z0, z1), x2)))
   MARK(add(x0, cons(dbl(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(cons(dbl(z0), x2)))
   MARK(add(x0, cons(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2)))
   MARK(add(x0, cons(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2)))
   MARK(add(x0, cons(recip(z0), x2))) -> c17(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(cons(recip(z0), x2)))
   MARK(add(x0, cons(s(z0), x2))) -> c17(A__ADD(mark(x0), cons(s(z0), x2)), MARK(cons(s(z0), x2)))
   MARK(add(x0, cons(0, x2))) -> c17(A__ADD(mark(x0), cons(0, x2)), MARK(cons(0, x2)))
   MARK(add(x0, cons(nil, x2))) -> c17(A__ADD(mark(x0), cons(nil, x2)), MARK(cons(nil, x2)))
   MARK(add(terms(z0), cons(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(sqr(z0), cons(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(add(z0, z1), cons(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(dbl(z0), cons(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(first(z0, z1), cons(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(0, cons(x1, x2))) -> c17(A__ADD(0, cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(x0, cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
   MARK(add(cons(z0, z1), cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
   MARK(add(recip(z0), cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
   MARK(add(s(z0), cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
   MARK(add(nil, cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
   MARK(add(x0, recip(terms(z0)))) -> c17(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(recip(terms(z0))))
   MARK(add(x0, recip(sqr(z0)))) -> c17(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(recip(sqr(z0))))
   MARK(add(x0, recip(add(z0, z1)))) -> c17(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(recip(add(z0, z1))))
   MARK(add(x0, recip(dbl(z0)))) -> c17(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(recip(dbl(z0))))
   MARK(add(x0, recip(first(z0, z1)))) -> c17(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(recip(first(z0, z1))))
   MARK(add(x0, recip(cons(z0, z1)))) -> c17(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(recip(cons(z0, z1))))
   MARK(add(x0, recip(recip(z0)))) -> c17(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(recip(recip(z0))))
   MARK(add(x0, recip(s(z0)))) -> c17(A__ADD(mark(x0), recip(s(z0))), MARK(recip(s(z0))))
   MARK(add(x0, recip(0))) -> c17(A__ADD(mark(x0), recip(0)), MARK(recip(0)))
   MARK(add(x0, recip(nil))) -> c17(A__ADD(mark(x0), recip(nil)), MARK(recip(nil)))
   MARK(add(terms(z0), recip(x1))) -> c17(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(sqr(z0), recip(x1))) -> c17(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(add(z0, z1), recip(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(dbl(z0), recip(x1))) -> c17(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(first(z0, z1), recip(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(0, recip(x1))) -> c17(A__ADD(0, recip(mark(x1))), MARK(recip(x1)))
   MARK(add(x0, recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(cons(z0, z1), recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(recip(z0), recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(s(z0), recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(nil, recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(terms(terms(z0)), x1)) -> c17(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(terms(sqr(z0)), x1)) -> c17(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(terms(add(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(terms(dbl(z0)), x1)) -> c17(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(terms(first(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(terms(cons(z0, z1)), x1)) -> c17(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(x1))
   MARK(add(terms(recip(z0)), x1)) -> c17(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(terms(s(z0)), x1)) -> c17(A__ADD(a__terms(s(z0)), mark(x1)), MARK(x1))
   MARK(add(terms(0), x1)) -> c17(A__ADD(a__terms(0), mark(x1)), MARK(x1))
   MARK(add(terms(nil), x1)) -> c17(A__ADD(a__terms(nil), mark(x1)), MARK(x1))
   MARK(add(terms(x0), s(z0))) -> c17(A__ADD(a__terms(mark(x0)), s(z0)))
   MARK(add(terms(x0), 0)) -> c17(A__ADD(a__terms(mark(x0)), 0))
   MARK(add(terms(x0), nil)) -> c17(A__ADD(a__terms(mark(x0)), nil))
   MARK(add(terms(x0), x1)) -> c17(MARK(x1))
   MARK(add(sqr(terms(z0)), x1)) -> c17(A__ADD(a__sqr(a__terms(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(sqr(sqr(z0)), x1)) -> c17(A__ADD(a__sqr(a__sqr(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(sqr(add(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(sqr(dbl(z0)), x1)) -> c17(A__ADD(a__sqr(a__dbl(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(sqr(first(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(sqr(cons(z0, z1)), x1)) -> c17(A__ADD(a__sqr(cons(mark(z0), z1)), mark(x1)), MARK(x1))
   MARK(add(sqr(recip(z0)), x1)) -> c17(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(sqr(s(z0)), x1)) -> c17(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(0), x1)) -> c17(A__ADD(a__sqr(0), mark(x1)), MARK(x1))
   MARK(add(sqr(nil), x1)) -> c17(A__ADD(a__sqr(nil), mark(x1)), MARK(x1))
   MARK(add(sqr(x0), s(z0))) -> c17(A__ADD(a__sqr(mark(x0)), s(z0)))
   MARK(add(sqr(x0), 0)) -> c17(A__ADD(a__sqr(mark(x0)), 0))
   MARK(add(sqr(x0), nil)) -> c17(A__ADD(a__sqr(mark(x0)), nil))
   MARK(add(sqr(x0), x1)) -> c17(MARK(x1))
   MARK(add(add(x0, terms(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(add(x0, sqr(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(add(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   MARK(add(add(x0, dbl(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(add(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   MARK(add(add(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2))
   MARK(add(add(x0, recip(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(add(x0, s(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), s(z0)), mark(x2)), MARK(x2))
   MARK(add(add(x0, 0), x2)) -> c17(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(x2))
   MARK(add(add(x0, nil), x2)) -> c17(A__ADD(a__add(mark(x0), nil), mark(x2)), MARK(x2))
   MARK(add(add(terms(z0), x1), x2)) -> c17(A__ADD(a__add(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(sqr(z0), x1), x2)) -> c17(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(add(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(dbl(z0), x1), x2)) -> c17(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(first(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(recip(z0), x1), x2)) -> c17(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(s(z0), x1), x2)) -> c17(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(0, x1), x2)) -> c17(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(nil, x1), x2)) -> c17(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(x0, x1), s(z0))) -> c17(A__ADD(a__add(mark(x0), mark(x1)), s(z0)))
   MARK(add(add(x0, x1), 0)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), 0))
   MARK(add(add(x0, x1), nil)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), nil))
   MARK(add(add(x0, x1), x2)) -> c17(MARK(x2))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2


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

(171) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) by 
   MARK(add(dbl(x0), terms(z0))) -> c17(A__ADD(a__dbl(mark(x0)), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(dbl(x0), sqr(z0))) -> c17(A__ADD(a__dbl(mark(x0)), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(dbl(x0), add(z0, z1))) -> c17(A__ADD(a__dbl(mark(x0)), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(dbl(x0), dbl(z0))) -> c17(A__ADD(a__dbl(mark(x0)), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(dbl(x0), first(z0, z1))) -> c17(A__ADD(a__dbl(mark(x0)), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(dbl(x0), cons(z0, z1))) -> c17(A__ADD(a__dbl(mark(x0)), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(dbl(x0), recip(z0))) -> c17(A__ADD(a__dbl(mark(x0)), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(dbl(x0), s(z0))) -> c17(A__ADD(a__dbl(mark(x0)), s(z0)), MARK(s(z0)))
   MARK(add(dbl(x0), 0)) -> c17(A__ADD(a__dbl(mark(x0)), 0), MARK(0))
   MARK(add(dbl(x0), nil)) -> c17(A__ADD(a__dbl(mark(x0)), nil), MARK(nil))
   MARK(add(dbl(x0), x1)) -> c17(A__ADD(dbl(mark(x0)), mark(x1)), MARK(x1))
   MARK(add(dbl(terms(z0)), x1)) -> c17(A__ADD(a__dbl(a__terms(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(sqr(z0)), x1)) -> c17(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(add(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(dbl(dbl(z0)), x1)) -> c17(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(first(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(dbl(cons(z0, z1)), x1)) -> c17(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(recip(z0)), x1)) -> c17(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(s(z0)), x1)) -> c17(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(x1))
   MARK(add(dbl(0), x1)) -> c17(A__ADD(a__dbl(0), mark(x1)), MARK(x1))
   MARK(add(dbl(nil), x1)) -> c17(A__ADD(a__dbl(nil), mark(x1)), MARK(x1))

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

(172)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2))))
   MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0))
   MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0))
   MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0))
   MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0))
   MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1))))
   MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0))
   MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0))
   MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0))
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   MARK(add(x0, recip(dbl(z0)))) -> c17(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(recip(dbl(z0))))
   MARK(add(x0, recip(first(z0, z1)))) -> c17(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(recip(first(z0, z1))))
   MARK(add(x0, recip(cons(z0, z1)))) -> c17(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(recip(cons(z0, z1))))
   MARK(add(x0, recip(recip(z0)))) -> c17(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(recip(recip(z0))))
   MARK(add(x0, recip(s(z0)))) -> c17(A__ADD(mark(x0), recip(s(z0))), MARK(recip(s(z0))))
   MARK(add(x0, recip(0))) -> c17(A__ADD(mark(x0), recip(0)), MARK(recip(0)))
   MARK(add(x0, recip(nil))) -> c17(A__ADD(mark(x0), recip(nil)), MARK(recip(nil)))
   MARK(add(terms(z0), recip(x1))) -> c17(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(sqr(z0), recip(x1))) -> c17(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(add(z0, z1), recip(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(dbl(z0), recip(x1))) -> c17(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(first(z0, z1), recip(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(0, recip(x1))) -> c17(A__ADD(0, recip(mark(x1))), MARK(recip(x1)))
   MARK(add(x0, recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(cons(z0, z1), recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(recip(z0), recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(s(z0), recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(nil, recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(terms(terms(z0)), x1)) -> c17(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(terms(sqr(z0)), x1)) -> c17(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(terms(add(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(terms(dbl(z0)), x1)) -> c17(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(terms(first(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(terms(cons(z0, z1)), x1)) -> c17(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(x1))
   MARK(add(terms(recip(z0)), x1)) -> c17(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(terms(s(z0)), x1)) -> c17(A__ADD(a__terms(s(z0)), mark(x1)), MARK(x1))
   MARK(add(terms(0), x1)) -> c17(A__ADD(a__terms(0), mark(x1)), MARK(x1))
   MARK(add(terms(nil), x1)) -> c17(A__ADD(a__terms(nil), mark(x1)), MARK(x1))
   MARK(add(terms(x0), s(z0))) -> c17(A__ADD(a__terms(mark(x0)), s(z0)))
   MARK(add(terms(x0), 0)) -> c17(A__ADD(a__terms(mark(x0)), 0))
   MARK(add(terms(x0), nil)) -> c17(A__ADD(a__terms(mark(x0)), nil))
   MARK(add(terms(x0), x1)) -> c17(MARK(x1))
   MARK(add(sqr(terms(z0)), x1)) -> c17(A__ADD(a__sqr(a__terms(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(sqr(sqr(z0)), x1)) -> c17(A__ADD(a__sqr(a__sqr(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(sqr(add(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(sqr(dbl(z0)), x1)) -> c17(A__ADD(a__sqr(a__dbl(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(sqr(first(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(sqr(cons(z0, z1)), x1)) -> c17(A__ADD(a__sqr(cons(mark(z0), z1)), mark(x1)), MARK(x1))
   MARK(add(sqr(recip(z0)), x1)) -> c17(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(sqr(s(z0)), x1)) -> c17(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(0), x1)) -> c17(A__ADD(a__sqr(0), mark(x1)), MARK(x1))
   MARK(add(sqr(nil), x1)) -> c17(A__ADD(a__sqr(nil), mark(x1)), MARK(x1))
   MARK(add(sqr(x0), s(z0))) -> c17(A__ADD(a__sqr(mark(x0)), s(z0)))
   MARK(add(sqr(x0), 0)) -> c17(A__ADD(a__sqr(mark(x0)), 0))
   MARK(add(sqr(x0), nil)) -> c17(A__ADD(a__sqr(mark(x0)), nil))
   MARK(add(sqr(x0), x1)) -> c17(MARK(x1))
   MARK(add(add(x0, terms(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(add(x0, sqr(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(add(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   MARK(add(add(x0, dbl(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(add(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   MARK(add(add(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2))
   MARK(add(add(x0, recip(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(add(x0, s(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), s(z0)), mark(x2)), MARK(x2))
   MARK(add(add(x0, 0), x2)) -> c17(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(x2))
   MARK(add(add(x0, nil), x2)) -> c17(A__ADD(a__add(mark(x0), nil), mark(x2)), MARK(x2))
   MARK(add(add(terms(z0), x1), x2)) -> c17(A__ADD(a__add(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(sqr(z0), x1), x2)) -> c17(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(add(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(dbl(z0), x1), x2)) -> c17(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(first(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(recip(z0), x1), x2)) -> c17(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(s(z0), x1), x2)) -> c17(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(0, x1), x2)) -> c17(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(nil, x1), x2)) -> c17(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(x0, x1), s(z0))) -> c17(A__ADD(a__add(mark(x0), mark(x1)), s(z0)))
   MARK(add(add(x0, x1), 0)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), 0))
   MARK(add(add(x0, x1), nil)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), nil))
   MARK(add(add(x0, x1), x2)) -> c17(MARK(x2))
   MARK(add(dbl(x0), s(z0))) -> c17(A__ADD(a__dbl(mark(x0)), s(z0)), MARK(s(z0)))
   MARK(add(dbl(x0), 0)) -> c17(A__ADD(a__dbl(mark(x0)), 0), MARK(0))
   MARK(add(dbl(x0), nil)) -> c17(A__ADD(a__dbl(mark(x0)), nil), MARK(nil))
   MARK(add(dbl(x0), x1)) -> c17(A__ADD(dbl(mark(x0)), mark(x1)), MARK(x1))
   MARK(add(dbl(terms(z0)), x1)) -> c17(A__ADD(a__dbl(a__terms(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(sqr(z0)), x1)) -> c17(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(add(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(dbl(dbl(z0)), x1)) -> c17(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(first(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(dbl(cons(z0, z1)), x1)) -> c17(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(recip(z0)), x1)) -> c17(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(s(z0)), x1)) -> c17(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(x1))
   MARK(add(dbl(0), x1)) -> c17(A__ADD(a__dbl(0), mark(x1)), MARK(x1))
   MARK(add(dbl(nil), x1)) -> c17(A__ADD(a__dbl(nil), mark(x1)), MARK(x1))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
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   MARK(add(x0, recip(recip(z0)))) -> c17(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(recip(recip(z0))))
   MARK(add(x0, recip(s(z0)))) -> c17(A__ADD(mark(x0), recip(s(z0))), MARK(recip(s(z0))))
   MARK(add(x0, recip(0))) -> c17(A__ADD(mark(x0), recip(0)), MARK(recip(0)))
   MARK(add(x0, recip(nil))) -> c17(A__ADD(mark(x0), recip(nil)), MARK(recip(nil)))
   MARK(add(terms(z0), recip(x1))) -> c17(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(sqr(z0), recip(x1))) -> c17(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(add(z0, z1), recip(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(dbl(z0), recip(x1))) -> c17(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(first(z0, z1), recip(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(0, recip(x1))) -> c17(A__ADD(0, recip(mark(x1))), MARK(recip(x1)))
   MARK(add(x0, recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(cons(z0, z1), recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(recip(z0), recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(s(z0), recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(nil, recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(terms(terms(z0)), x1)) -> c17(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(terms(sqr(z0)), x1)) -> c17(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(terms(add(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(terms(dbl(z0)), x1)) -> c17(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(terms(first(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(terms(cons(z0, z1)), x1)) -> c17(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(x1))
   MARK(add(terms(recip(z0)), x1)) -> c17(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(terms(s(z0)), x1)) -> c17(A__ADD(a__terms(s(z0)), mark(x1)), MARK(x1))
   MARK(add(terms(0), x1)) -> c17(A__ADD(a__terms(0), mark(x1)), MARK(x1))
   MARK(add(terms(nil), x1)) -> c17(A__ADD(a__terms(nil), mark(x1)), MARK(x1))
   MARK(add(terms(x0), s(z0))) -> c17(A__ADD(a__terms(mark(x0)), s(z0)))
   MARK(add(terms(x0), 0)) -> c17(A__ADD(a__terms(mark(x0)), 0))
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   MARK(add(sqr(sqr(z0)), x1)) -> c17(A__ADD(a__sqr(a__sqr(mark(z0))), mark(x1)), MARK(x1))
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   MARK(add(sqr(cons(z0, z1)), x1)) -> c17(A__ADD(a__sqr(cons(mark(z0), z1)), mark(x1)), MARK(x1))
   MARK(add(sqr(recip(z0)), x1)) -> c17(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(sqr(s(z0)), x1)) -> c17(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(0), x1)) -> c17(A__ADD(a__sqr(0), mark(x1)), MARK(x1))
   MARK(add(sqr(nil), x1)) -> c17(A__ADD(a__sqr(nil), mark(x1)), MARK(x1))
   MARK(add(sqr(x0), s(z0))) -> c17(A__ADD(a__sqr(mark(x0)), s(z0)))
   MARK(add(sqr(x0), 0)) -> c17(A__ADD(a__sqr(mark(x0)), 0))
   MARK(add(sqr(x0), nil)) -> c17(A__ADD(a__sqr(mark(x0)), nil))
   MARK(add(sqr(x0), x1)) -> c17(MARK(x1))
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   MARK(add(add(first(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
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   MARK(add(add(x0, x1), 0)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), 0))
   MARK(add(add(x0, x1), nil)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), nil))
   MARK(add(add(x0, x1), x2)) -> c17(MARK(x2))
   MARK(add(dbl(x0), s(z0))) -> c17(A__ADD(a__dbl(mark(x0)), s(z0)), MARK(s(z0)))
   MARK(add(dbl(x0), 0)) -> c17(A__ADD(a__dbl(mark(x0)), 0), MARK(0))
   MARK(add(dbl(x0), nil)) -> c17(A__ADD(a__dbl(mark(x0)), nil), MARK(nil))
   MARK(add(dbl(x0), x1)) -> c17(A__ADD(dbl(mark(x0)), mark(x1)), MARK(x1))
   MARK(add(dbl(terms(z0)), x1)) -> c17(A__ADD(a__dbl(a__terms(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(sqr(z0)), x1)) -> c17(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(add(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(dbl(dbl(z0)), x1)) -> c17(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(first(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(dbl(cons(z0, z1)), x1)) -> c17(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(recip(z0)), x1)) -> c17(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(s(z0)), x1)) -> c17(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(x1))
   MARK(add(dbl(0), x1)) -> c17(A__ADD(a__dbl(0), mark(x1)), MARK(x1))
   MARK(add(dbl(nil), x1)) -> c17(A__ADD(a__dbl(nil), mark(x1)), MARK(x1))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2


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

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

(174)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
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   MARK(add(terms(cons(z0, z1)), x1)) -> c17(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(x1))
   MARK(add(terms(recip(z0)), x1)) -> c17(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(terms(s(z0)), x1)) -> c17(A__ADD(a__terms(s(z0)), mark(x1)), MARK(x1))
   MARK(add(terms(0), x1)) -> c17(A__ADD(a__terms(0), mark(x1)), MARK(x1))
   MARK(add(terms(nil), x1)) -> c17(A__ADD(a__terms(nil), mark(x1)), MARK(x1))
   MARK(add(terms(x0), s(z0))) -> c17(A__ADD(a__terms(mark(x0)), s(z0)))
   MARK(add(terms(x0), 0)) -> c17(A__ADD(a__terms(mark(x0)), 0))
   MARK(add(terms(x0), nil)) -> c17(A__ADD(a__terms(mark(x0)), nil))
   MARK(add(terms(x0), x1)) -> c17(MARK(x1))
   MARK(add(sqr(terms(z0)), x1)) -> c17(A__ADD(a__sqr(a__terms(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(sqr(sqr(z0)), x1)) -> c17(A__ADD(a__sqr(a__sqr(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(sqr(add(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(sqr(dbl(z0)), x1)) -> c17(A__ADD(a__sqr(a__dbl(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(sqr(first(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(sqr(cons(z0, z1)), x1)) -> c17(A__ADD(a__sqr(cons(mark(z0), z1)), mark(x1)), MARK(x1))
   MARK(add(sqr(recip(z0)), x1)) -> c17(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(sqr(s(z0)), x1)) -> c17(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(0), x1)) -> c17(A__ADD(a__sqr(0), mark(x1)), MARK(x1))
   MARK(add(sqr(nil), x1)) -> c17(A__ADD(a__sqr(nil), mark(x1)), MARK(x1))
   MARK(add(sqr(x0), s(z0))) -> c17(A__ADD(a__sqr(mark(x0)), s(z0)))
   MARK(add(sqr(x0), 0)) -> c17(A__ADD(a__sqr(mark(x0)), 0))
   MARK(add(sqr(x0), nil)) -> c17(A__ADD(a__sqr(mark(x0)), nil))
   MARK(add(sqr(x0), x1)) -> c17(MARK(x1))
   MARK(add(add(x0, terms(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(add(x0, sqr(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(add(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   MARK(add(add(x0, dbl(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(add(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   MARK(add(add(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2))
   MARK(add(add(x0, recip(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(add(x0, s(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), s(z0)), mark(x2)), MARK(x2))
   MARK(add(add(x0, 0), x2)) -> c17(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(x2))
   MARK(add(add(x0, nil), x2)) -> c17(A__ADD(a__add(mark(x0), nil), mark(x2)), MARK(x2))
   MARK(add(add(terms(z0), x1), x2)) -> c17(A__ADD(a__add(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(sqr(z0), x1), x2)) -> c17(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(add(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(dbl(z0), x1), x2)) -> c17(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(first(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(recip(z0), x1), x2)) -> c17(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(s(z0), x1), x2)) -> c17(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(0, x1), x2)) -> c17(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(nil, x1), x2)) -> c17(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(x0, x1), s(z0))) -> c17(A__ADD(a__add(mark(x0), mark(x1)), s(z0)))
   MARK(add(add(x0, x1), 0)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), 0))
   MARK(add(add(x0, x1), nil)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), nil))
   MARK(add(add(x0, x1), x2)) -> c17(MARK(x2))
   MARK(add(dbl(terms(z0)), x1)) -> c17(A__ADD(a__dbl(a__terms(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(sqr(z0)), x1)) -> c17(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(add(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(dbl(dbl(z0)), x1)) -> c17(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(first(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(dbl(cons(z0, z1)), x1)) -> c17(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(recip(z0)), x1)) -> c17(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(s(z0)), x1)) -> c17(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(x1))
   MARK(add(dbl(0), x1)) -> c17(A__ADD(a__dbl(0), mark(x1)), MARK(x1))
   MARK(add(dbl(nil), x1)) -> c17(A__ADD(a__dbl(nil), mark(x1)), MARK(x1))
   MARK(add(dbl(x0), s(z0))) -> c17(A__ADD(a__dbl(mark(x0)), s(z0)))
   MARK(add(dbl(x0), 0)) -> c17(A__ADD(a__dbl(mark(x0)), 0))
   MARK(add(dbl(x0), nil)) -> c17(A__ADD(a__dbl(mark(x0)), nil))
   MARK(add(dbl(x0), x1)) -> c17(MARK(x1))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0))
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   MARK(add(x0, first(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2)))
   MARK(add(x0, first(recip(z0), x2))) -> c17(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(first(recip(z0), x2)))
   MARK(add(x0, first(s(z0), x2))) -> c17(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(first(s(z0), x2)))
   MARK(add(x0, first(0, x2))) -> c17(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2)))
   MARK(add(x0, first(nil, x2))) -> c17(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2)))
   MARK(add(terms(z0), first(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(sqr(z0), first(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(add(z0, z1), first(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(dbl(z0), first(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(first(z0, z1), first(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(0, first(x1, x2))) -> c17(A__ADD(0, a__first(mark(x1), mark(x2))), MARK(first(x1, x2)))
   MARK(add(cons(z0, z1), first(x1, x2))) -> c17(MARK(first(x1, x2)))
   MARK(add(recip(z0), first(x1, x2))) -> c17(MARK(first(x1, x2)))
   MARK(add(s(z0), first(x1, x2))) -> c17(MARK(first(x1, x2)))
   MARK(add(nil, first(x1, x2))) -> c17(MARK(first(x1, x2)))
   MARK(add(x0, cons(terms(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(cons(terms(z0), x2)))
   MARK(add(x0, cons(sqr(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(cons(sqr(z0), x2)))
   MARK(add(x0, cons(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(cons(add(z0, z1), x2)))
   MARK(add(x0, cons(dbl(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(cons(dbl(z0), x2)))
   MARK(add(x0, cons(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2)))
   MARK(add(x0, cons(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2)))
   MARK(add(x0, cons(recip(z0), x2))) -> c17(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(cons(recip(z0), x2)))
   MARK(add(x0, cons(s(z0), x2))) -> c17(A__ADD(mark(x0), cons(s(z0), x2)), MARK(cons(s(z0), x2)))
   MARK(add(x0, cons(0, x2))) -> c17(A__ADD(mark(x0), cons(0, x2)), MARK(cons(0, x2)))
   MARK(add(x0, cons(nil, x2))) -> c17(A__ADD(mark(x0), cons(nil, x2)), MARK(cons(nil, x2)))
   MARK(add(terms(z0), cons(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(sqr(z0), cons(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(add(z0, z1), cons(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(dbl(z0), cons(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(first(z0, z1), cons(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(0, cons(x1, x2))) -> c17(A__ADD(0, cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(x0, cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
   MARK(add(cons(z0, z1), cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
   MARK(add(recip(z0), cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
   MARK(add(s(z0), cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
   MARK(add(nil, cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
   MARK(add(x0, recip(terms(z0)))) -> c17(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(recip(terms(z0))))
   MARK(add(x0, recip(sqr(z0)))) -> c17(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(recip(sqr(z0))))
   MARK(add(x0, recip(add(z0, z1)))) -> c17(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(recip(add(z0, z1))))
   MARK(add(x0, recip(dbl(z0)))) -> c17(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(recip(dbl(z0))))
   MARK(add(x0, recip(first(z0, z1)))) -> c17(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(recip(first(z0, z1))))
   MARK(add(x0, recip(cons(z0, z1)))) -> c17(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(recip(cons(z0, z1))))
   MARK(add(x0, recip(recip(z0)))) -> c17(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(recip(recip(z0))))
   MARK(add(x0, recip(s(z0)))) -> c17(A__ADD(mark(x0), recip(s(z0))), MARK(recip(s(z0))))
   MARK(add(x0, recip(0))) -> c17(A__ADD(mark(x0), recip(0)), MARK(recip(0)))
   MARK(add(x0, recip(nil))) -> c17(A__ADD(mark(x0), recip(nil)), MARK(recip(nil)))
   MARK(add(terms(z0), recip(x1))) -> c17(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(sqr(z0), recip(x1))) -> c17(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(add(z0, z1), recip(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(dbl(z0), recip(x1))) -> c17(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(first(z0, z1), recip(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(0, recip(x1))) -> c17(A__ADD(0, recip(mark(x1))), MARK(recip(x1)))
   MARK(add(x0, recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(cons(z0, z1), recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(recip(z0), recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(s(z0), recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(nil, recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(terms(terms(z0)), x1)) -> c17(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(terms(sqr(z0)), x1)) -> c17(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(terms(add(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(terms(dbl(z0)), x1)) -> c17(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(terms(first(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(terms(cons(z0, z1)), x1)) -> c17(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(x1))
   MARK(add(terms(recip(z0)), x1)) -> c17(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(terms(s(z0)), x1)) -> c17(A__ADD(a__terms(s(z0)), mark(x1)), MARK(x1))
   MARK(add(terms(0), x1)) -> c17(A__ADD(a__terms(0), mark(x1)), MARK(x1))
   MARK(add(terms(nil), x1)) -> c17(A__ADD(a__terms(nil), mark(x1)), MARK(x1))
   MARK(add(terms(x0), s(z0))) -> c17(A__ADD(a__terms(mark(x0)), s(z0)))
   MARK(add(terms(x0), 0)) -> c17(A__ADD(a__terms(mark(x0)), 0))
   MARK(add(terms(x0), nil)) -> c17(A__ADD(a__terms(mark(x0)), nil))
   MARK(add(terms(x0), x1)) -> c17(MARK(x1))
   MARK(add(sqr(terms(z0)), x1)) -> c17(A__ADD(a__sqr(a__terms(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(sqr(sqr(z0)), x1)) -> c17(A__ADD(a__sqr(a__sqr(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(sqr(add(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(sqr(dbl(z0)), x1)) -> c17(A__ADD(a__sqr(a__dbl(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(sqr(first(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(sqr(cons(z0, z1)), x1)) -> c17(A__ADD(a__sqr(cons(mark(z0), z1)), mark(x1)), MARK(x1))
   MARK(add(sqr(recip(z0)), x1)) -> c17(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(sqr(s(z0)), x1)) -> c17(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(0), x1)) -> c17(A__ADD(a__sqr(0), mark(x1)), MARK(x1))
   MARK(add(sqr(nil), x1)) -> c17(A__ADD(a__sqr(nil), mark(x1)), MARK(x1))
   MARK(add(sqr(x0), s(z0))) -> c17(A__ADD(a__sqr(mark(x0)), s(z0)))
   MARK(add(sqr(x0), 0)) -> c17(A__ADD(a__sqr(mark(x0)), 0))
   MARK(add(sqr(x0), nil)) -> c17(A__ADD(a__sqr(mark(x0)), nil))
   MARK(add(sqr(x0), x1)) -> c17(MARK(x1))
   MARK(add(add(x0, terms(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(add(x0, sqr(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(add(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   MARK(add(add(x0, dbl(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(add(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   MARK(add(add(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2))
   MARK(add(add(x0, recip(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(add(x0, s(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), s(z0)), mark(x2)), MARK(x2))
   MARK(add(add(x0, 0), x2)) -> c17(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(x2))
   MARK(add(add(x0, nil), x2)) -> c17(A__ADD(a__add(mark(x0), nil), mark(x2)), MARK(x2))
   MARK(add(add(terms(z0), x1), x2)) -> c17(A__ADD(a__add(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(sqr(z0), x1), x2)) -> c17(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(add(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(dbl(z0), x1), x2)) -> c17(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(first(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(recip(z0), x1), x2)) -> c17(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(s(z0), x1), x2)) -> c17(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(0, x1), x2)) -> c17(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(nil, x1), x2)) -> c17(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(x0, x1), s(z0))) -> c17(A__ADD(a__add(mark(x0), mark(x1)), s(z0)))
   MARK(add(add(x0, x1), 0)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), 0))
   MARK(add(add(x0, x1), nil)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), nil))
   MARK(add(add(x0, x1), x2)) -> c17(MARK(x2))
   MARK(add(dbl(terms(z0)), x1)) -> c17(A__ADD(a__dbl(a__terms(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(sqr(z0)), x1)) -> c17(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(add(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(dbl(dbl(z0)), x1)) -> c17(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(first(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(dbl(cons(z0, z1)), x1)) -> c17(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(recip(z0)), x1)) -> c17(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(s(z0)), x1)) -> c17(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(x1))
   MARK(add(dbl(0), x1)) -> c17(A__ADD(a__dbl(0), mark(x1)), MARK(x1))
   MARK(add(dbl(nil), x1)) -> c17(A__ADD(a__dbl(nil), mark(x1)), MARK(x1))
   MARK(add(dbl(x0), s(z0))) -> c17(A__ADD(a__dbl(mark(x0)), s(z0)))
   MARK(add(dbl(x0), 0)) -> c17(A__ADD(a__dbl(mark(x0)), 0))
   MARK(add(dbl(x0), nil)) -> c17(A__ADD(a__dbl(mark(x0)), nil))
   MARK(add(dbl(x0), x1)) -> c17(MARK(x1))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2


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

(175) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) by 
   MARK(add(first(x0, x1), terms(z0))) -> c17(A__ADD(a__first(mark(x0), mark(x1)), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(add(first(x0, x1), sqr(z0))) -> c17(A__ADD(a__first(mark(x0), mark(x1)), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(add(first(x0, x1), add(z0, z1))) -> c17(A__ADD(a__first(mark(x0), mark(x1)), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(add(first(x0, x1), dbl(z0))) -> c17(A__ADD(a__first(mark(x0), mark(x1)), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(add(first(x0, x1), first(z0, z1))) -> c17(A__ADD(a__first(mark(x0), mark(x1)), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(add(first(x0, x1), cons(z0, z1))) -> c17(A__ADD(a__first(mark(x0), mark(x1)), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(add(first(x0, x1), recip(z0))) -> c17(A__ADD(a__first(mark(x0), mark(x1)), recip(mark(z0))), MARK(recip(z0)))
   MARK(add(first(x0, x1), s(z0))) -> c17(A__ADD(a__first(mark(x0), mark(x1)), s(z0)), MARK(s(z0)))
   MARK(add(first(x0, x1), 0)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), 0), MARK(0))
   MARK(add(first(x0, x1), nil)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), nil), MARK(nil))
   MARK(add(first(x0, x1), x2)) -> c17(A__ADD(first(mark(x0), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(x0, terms(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, sqr(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   MARK(add(first(x0, dbl(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   MARK(add(first(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2))
   MARK(add(first(x0, recip(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, s(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(x2))
   MARK(add(first(x0, 0), x2)) -> c17(A__ADD(a__first(mark(x0), 0), mark(x2)), MARK(x2))
   MARK(add(first(x0, nil), x2)) -> c17(A__ADD(a__first(mark(x0), nil), mark(x2)), MARK(x2))
   MARK(add(first(terms(z0), x1), x2)) -> c17(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(sqr(z0), x1), x2)) -> c17(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(add(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(dbl(z0), x1), x2)) -> c17(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(first(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(recip(z0), x1), x2)) -> c17(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(s(z0), x1), x2)) -> c17(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(0, x1), x2)) -> c17(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(nil, x1), x2)) -> c17(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(x2))

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

(176)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2))))
   MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0))
   MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0))
   MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0))
   MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0))
   MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1))))
   MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0))
   MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0))
   MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0))
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   MARK(add(terms(z0), recip(x1))) -> c17(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(sqr(z0), recip(x1))) -> c17(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(add(z0, z1), recip(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(dbl(z0), recip(x1))) -> c17(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(first(z0, z1), recip(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(0, recip(x1))) -> c17(A__ADD(0, recip(mark(x1))), MARK(recip(x1)))
   MARK(add(x0, recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(cons(z0, z1), recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(recip(z0), recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(s(z0), recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(nil, recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(terms(terms(z0)), x1)) -> c17(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(terms(sqr(z0)), x1)) -> c17(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(terms(add(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(terms(dbl(z0)), x1)) -> c17(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(terms(first(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(terms(cons(z0, z1)), x1)) -> c17(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(x1))
   MARK(add(terms(recip(z0)), x1)) -> c17(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(terms(s(z0)), x1)) -> c17(A__ADD(a__terms(s(z0)), mark(x1)), MARK(x1))
   MARK(add(terms(0), x1)) -> c17(A__ADD(a__terms(0), mark(x1)), MARK(x1))
   MARK(add(terms(nil), x1)) -> c17(A__ADD(a__terms(nil), mark(x1)), MARK(x1))
   MARK(add(terms(x0), s(z0))) -> c17(A__ADD(a__terms(mark(x0)), s(z0)))
   MARK(add(terms(x0), 0)) -> c17(A__ADD(a__terms(mark(x0)), 0))
   MARK(add(terms(x0), nil)) -> c17(A__ADD(a__terms(mark(x0)), nil))
   MARK(add(terms(x0), x1)) -> c17(MARK(x1))
   MARK(add(sqr(terms(z0)), x1)) -> c17(A__ADD(a__sqr(a__terms(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(sqr(sqr(z0)), x1)) -> c17(A__ADD(a__sqr(a__sqr(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(sqr(add(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(sqr(dbl(z0)), x1)) -> c17(A__ADD(a__sqr(a__dbl(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(sqr(first(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(sqr(cons(z0, z1)), x1)) -> c17(A__ADD(a__sqr(cons(mark(z0), z1)), mark(x1)), MARK(x1))
   MARK(add(sqr(recip(z0)), x1)) -> c17(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(sqr(s(z0)), x1)) -> c17(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(0), x1)) -> c17(A__ADD(a__sqr(0), mark(x1)), MARK(x1))
   MARK(add(sqr(nil), x1)) -> c17(A__ADD(a__sqr(nil), mark(x1)), MARK(x1))
   MARK(add(sqr(x0), s(z0))) -> c17(A__ADD(a__sqr(mark(x0)), s(z0)))
   MARK(add(sqr(x0), 0)) -> c17(A__ADD(a__sqr(mark(x0)), 0))
   MARK(add(sqr(x0), nil)) -> c17(A__ADD(a__sqr(mark(x0)), nil))
   MARK(add(sqr(x0), x1)) -> c17(MARK(x1))
   MARK(add(add(x0, terms(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(add(x0, sqr(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(add(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   MARK(add(add(x0, dbl(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(add(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   MARK(add(add(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2))
   MARK(add(add(x0, recip(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(add(x0, s(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), s(z0)), mark(x2)), MARK(x2))
   MARK(add(add(x0, 0), x2)) -> c17(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(x2))
   MARK(add(add(x0, nil), x2)) -> c17(A__ADD(a__add(mark(x0), nil), mark(x2)), MARK(x2))
   MARK(add(add(terms(z0), x1), x2)) -> c17(A__ADD(a__add(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(sqr(z0), x1), x2)) -> c17(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(add(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(dbl(z0), x1), x2)) -> c17(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(first(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(recip(z0), x1), x2)) -> c17(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(s(z0), x1), x2)) -> c17(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(0, x1), x2)) -> c17(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(nil, x1), x2)) -> c17(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(x0, x1), s(z0))) -> c17(A__ADD(a__add(mark(x0), mark(x1)), s(z0)))
   MARK(add(add(x0, x1), 0)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), 0))
   MARK(add(add(x0, x1), nil)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), nil))
   MARK(add(add(x0, x1), x2)) -> c17(MARK(x2))
   MARK(add(dbl(terms(z0)), x1)) -> c17(A__ADD(a__dbl(a__terms(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(sqr(z0)), x1)) -> c17(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(add(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(dbl(dbl(z0)), x1)) -> c17(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(first(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(dbl(cons(z0, z1)), x1)) -> c17(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(recip(z0)), x1)) -> c17(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(s(z0)), x1)) -> c17(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(x1))
   MARK(add(dbl(0), x1)) -> c17(A__ADD(a__dbl(0), mark(x1)), MARK(x1))
   MARK(add(dbl(nil), x1)) -> c17(A__ADD(a__dbl(nil), mark(x1)), MARK(x1))
   MARK(add(dbl(x0), s(z0))) -> c17(A__ADD(a__dbl(mark(x0)), s(z0)))
   MARK(add(dbl(x0), 0)) -> c17(A__ADD(a__dbl(mark(x0)), 0))
   MARK(add(dbl(x0), nil)) -> c17(A__ADD(a__dbl(mark(x0)), nil))
   MARK(add(dbl(x0), x1)) -> c17(MARK(x1))
   MARK(add(first(x0, x1), s(z0))) -> c17(A__ADD(a__first(mark(x0), mark(x1)), s(z0)), MARK(s(z0)))
   MARK(add(first(x0, x1), 0)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), 0), MARK(0))
   MARK(add(first(x0, x1), nil)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), nil), MARK(nil))
   MARK(add(first(x0, x1), x2)) -> c17(A__ADD(first(mark(x0), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(x0, terms(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, sqr(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   MARK(add(first(x0, dbl(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   MARK(add(first(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2))
   MARK(add(first(x0, recip(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, s(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(x2))
   MARK(add(first(x0, 0), x2)) -> c17(A__ADD(a__first(mark(x0), 0), mark(x2)), MARK(x2))
   MARK(add(first(x0, nil), x2)) -> c17(A__ADD(a__first(mark(x0), nil), mark(x2)), MARK(x2))
   MARK(add(first(terms(z0), x1), x2)) -> c17(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(sqr(z0), x1), x2)) -> c17(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(add(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(dbl(z0), x1), x2)) -> c17(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(first(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(recip(z0), x1), x2)) -> c17(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(s(z0), x1), x2)) -> c17(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(0, x1), x2)) -> c17(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(nil, x1), x2)) -> c17(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(x2))
S tuples:
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   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
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   MARK(add(first(x0, x1), x2)) -> c17(A__ADD(first(mark(x0), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(x0, terms(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, sqr(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   MARK(add(first(x0, dbl(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   MARK(add(first(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2))
   MARK(add(first(x0, recip(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, s(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(x2))
   MARK(add(first(x0, 0), x2)) -> c17(A__ADD(a__first(mark(x0), 0), mark(x2)), MARK(x2))
   MARK(add(first(x0, nil), x2)) -> c17(A__ADD(a__first(mark(x0), nil), mark(x2)), MARK(x2))
   MARK(add(first(terms(z0), x1), x2)) -> c17(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(sqr(z0), x1), x2)) -> c17(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(add(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(dbl(z0), x1), x2)) -> c17(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(first(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(recip(z0), x1), x2)) -> c17(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(s(z0), x1), x2)) -> c17(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(0, x1), x2)) -> c17(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(nil, x1), x2)) -> c17(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(x2))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2


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

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

(178)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2))))
   MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0))
   MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0))
   MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0))
   MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0))
   MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0)))
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   MARK(add(x0, cons(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2)))
   MARK(add(x0, cons(recip(z0), x2))) -> c17(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(cons(recip(z0), x2)))
   MARK(add(x0, cons(s(z0), x2))) -> c17(A__ADD(mark(x0), cons(s(z0), x2)), MARK(cons(s(z0), x2)))
   MARK(add(x0, cons(0, x2))) -> c17(A__ADD(mark(x0), cons(0, x2)), MARK(cons(0, x2)))
   MARK(add(x0, cons(nil, x2))) -> c17(A__ADD(mark(x0), cons(nil, x2)), MARK(cons(nil, x2)))
   MARK(add(terms(z0), cons(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(sqr(z0), cons(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(add(z0, z1), cons(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(dbl(z0), cons(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(first(z0, z1), cons(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(0, cons(x1, x2))) -> c17(A__ADD(0, cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(x0, cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
   MARK(add(cons(z0, z1), cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
   MARK(add(recip(z0), cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
   MARK(add(s(z0), cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
   MARK(add(nil, cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
   MARK(add(x0, recip(terms(z0)))) -> c17(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(recip(terms(z0))))
   MARK(add(x0, recip(sqr(z0)))) -> c17(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(recip(sqr(z0))))
   MARK(add(x0, recip(add(z0, z1)))) -> c17(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(recip(add(z0, z1))))
   MARK(add(x0, recip(dbl(z0)))) -> c17(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(recip(dbl(z0))))
   MARK(add(x0, recip(first(z0, z1)))) -> c17(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(recip(first(z0, z1))))
   MARK(add(x0, recip(cons(z0, z1)))) -> c17(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(recip(cons(z0, z1))))
   MARK(add(x0, recip(recip(z0)))) -> c17(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(recip(recip(z0))))
   MARK(add(x0, recip(s(z0)))) -> c17(A__ADD(mark(x0), recip(s(z0))), MARK(recip(s(z0))))
   MARK(add(x0, recip(0))) -> c17(A__ADD(mark(x0), recip(0)), MARK(recip(0)))
   MARK(add(x0, recip(nil))) -> c17(A__ADD(mark(x0), recip(nil)), MARK(recip(nil)))
   MARK(add(terms(z0), recip(x1))) -> c17(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(sqr(z0), recip(x1))) -> c17(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(add(z0, z1), recip(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(dbl(z0), recip(x1))) -> c17(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(first(z0, z1), recip(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(0, recip(x1))) -> c17(A__ADD(0, recip(mark(x1))), MARK(recip(x1)))
   MARK(add(x0, recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(cons(z0, z1), recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(recip(z0), recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(s(z0), recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(nil, recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(terms(terms(z0)), x1)) -> c17(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(terms(sqr(z0)), x1)) -> c17(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(terms(add(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(terms(dbl(z0)), x1)) -> c17(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(terms(first(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(terms(cons(z0, z1)), x1)) -> c17(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(x1))
   MARK(add(terms(recip(z0)), x1)) -> c17(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(terms(s(z0)), x1)) -> c17(A__ADD(a__terms(s(z0)), mark(x1)), MARK(x1))
   MARK(add(terms(0), x1)) -> c17(A__ADD(a__terms(0), mark(x1)), MARK(x1))
   MARK(add(terms(nil), x1)) -> c17(A__ADD(a__terms(nil), mark(x1)), MARK(x1))
   MARK(add(terms(x0), s(z0))) -> c17(A__ADD(a__terms(mark(x0)), s(z0)))
   MARK(add(terms(x0), 0)) -> c17(A__ADD(a__terms(mark(x0)), 0))
   MARK(add(terms(x0), nil)) -> c17(A__ADD(a__terms(mark(x0)), nil))
   MARK(add(terms(x0), x1)) -> c17(MARK(x1))
   MARK(add(sqr(terms(z0)), x1)) -> c17(A__ADD(a__sqr(a__terms(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(sqr(sqr(z0)), x1)) -> c17(A__ADD(a__sqr(a__sqr(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(sqr(add(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(sqr(dbl(z0)), x1)) -> c17(A__ADD(a__sqr(a__dbl(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(sqr(first(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(sqr(cons(z0, z1)), x1)) -> c17(A__ADD(a__sqr(cons(mark(z0), z1)), mark(x1)), MARK(x1))
   MARK(add(sqr(recip(z0)), x1)) -> c17(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(sqr(s(z0)), x1)) -> c17(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(0), x1)) -> c17(A__ADD(a__sqr(0), mark(x1)), MARK(x1))
   MARK(add(sqr(nil), x1)) -> c17(A__ADD(a__sqr(nil), mark(x1)), MARK(x1))
   MARK(add(sqr(x0), s(z0))) -> c17(A__ADD(a__sqr(mark(x0)), s(z0)))
   MARK(add(sqr(x0), 0)) -> c17(A__ADD(a__sqr(mark(x0)), 0))
   MARK(add(sqr(x0), nil)) -> c17(A__ADD(a__sqr(mark(x0)), nil))
   MARK(add(sqr(x0), x1)) -> c17(MARK(x1))
   MARK(add(add(x0, terms(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(add(x0, sqr(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(add(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   MARK(add(add(x0, dbl(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(add(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   MARK(add(add(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2))
   MARK(add(add(x0, recip(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(add(x0, s(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), s(z0)), mark(x2)), MARK(x2))
   MARK(add(add(x0, 0), x2)) -> c17(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(x2))
   MARK(add(add(x0, nil), x2)) -> c17(A__ADD(a__add(mark(x0), nil), mark(x2)), MARK(x2))
   MARK(add(add(terms(z0), x1), x2)) -> c17(A__ADD(a__add(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(sqr(z0), x1), x2)) -> c17(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(add(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(dbl(z0), x1), x2)) -> c17(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(first(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(recip(z0), x1), x2)) -> c17(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(s(z0), x1), x2)) -> c17(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(0, x1), x2)) -> c17(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(nil, x1), x2)) -> c17(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(x0, x1), s(z0))) -> c17(A__ADD(a__add(mark(x0), mark(x1)), s(z0)))
   MARK(add(add(x0, x1), 0)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), 0))
   MARK(add(add(x0, x1), nil)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), nil))
   MARK(add(add(x0, x1), x2)) -> c17(MARK(x2))
   MARK(add(dbl(terms(z0)), x1)) -> c17(A__ADD(a__dbl(a__terms(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(sqr(z0)), x1)) -> c17(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(add(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(dbl(dbl(z0)), x1)) -> c17(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(first(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(dbl(cons(z0, z1)), x1)) -> c17(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(recip(z0)), x1)) -> c17(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(s(z0)), x1)) -> c17(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(x1))
   MARK(add(dbl(0), x1)) -> c17(A__ADD(a__dbl(0), mark(x1)), MARK(x1))
   MARK(add(dbl(nil), x1)) -> c17(A__ADD(a__dbl(nil), mark(x1)), MARK(x1))
   MARK(add(dbl(x0), s(z0))) -> c17(A__ADD(a__dbl(mark(x0)), s(z0)))
   MARK(add(dbl(x0), 0)) -> c17(A__ADD(a__dbl(mark(x0)), 0))
   MARK(add(dbl(x0), nil)) -> c17(A__ADD(a__dbl(mark(x0)), nil))
   MARK(add(dbl(x0), x1)) -> c17(MARK(x1))
   MARK(add(first(x0, terms(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, sqr(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   MARK(add(first(x0, dbl(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   MARK(add(first(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2))
   MARK(add(first(x0, recip(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, s(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(x2))
   MARK(add(first(x0, 0), x2)) -> c17(A__ADD(a__first(mark(x0), 0), mark(x2)), MARK(x2))
   MARK(add(first(x0, nil), x2)) -> c17(A__ADD(a__first(mark(x0), nil), mark(x2)), MARK(x2))
   MARK(add(first(terms(z0), x1), x2)) -> c17(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(sqr(z0), x1), x2)) -> c17(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(add(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(dbl(z0), x1), x2)) -> c17(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(first(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(recip(z0), x1), x2)) -> c17(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(s(z0), x1), x2)) -> c17(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(0, x1), x2)) -> c17(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(nil, x1), x2)) -> c17(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(x0, x1), s(z0))) -> c17(A__ADD(a__first(mark(x0), mark(x1)), s(z0)))
   MARK(add(first(x0, x1), 0)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), 0))
   MARK(add(first(x0, x1), nil)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), nil))
   MARK(add(first(x0, x1), x2)) -> c17(MARK(x2))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
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   MARK(add(add(first(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(recip(z0), x1), x2)) -> c17(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(s(z0), x1), x2)) -> c17(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(0, x1), x2)) -> c17(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(nil, x1), x2)) -> c17(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(x0, x1), s(z0))) -> c17(A__ADD(a__add(mark(x0), mark(x1)), s(z0)))
   MARK(add(add(x0, x1), 0)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), 0))
   MARK(add(add(x0, x1), nil)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), nil))
   MARK(add(add(x0, x1), x2)) -> c17(MARK(x2))
   MARK(add(dbl(terms(z0)), x1)) -> c17(A__ADD(a__dbl(a__terms(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(sqr(z0)), x1)) -> c17(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(add(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(dbl(dbl(z0)), x1)) -> c17(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(first(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(dbl(cons(z0, z1)), x1)) -> c17(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(recip(z0)), x1)) -> c17(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(s(z0)), x1)) -> c17(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(x1))
   MARK(add(dbl(0), x1)) -> c17(A__ADD(a__dbl(0), mark(x1)), MARK(x1))
   MARK(add(dbl(nil), x1)) -> c17(A__ADD(a__dbl(nil), mark(x1)), MARK(x1))
   MARK(add(dbl(x0), s(z0))) -> c17(A__ADD(a__dbl(mark(x0)), s(z0)))
   MARK(add(dbl(x0), 0)) -> c17(A__ADD(a__dbl(mark(x0)), 0))
   MARK(add(dbl(x0), nil)) -> c17(A__ADD(a__dbl(mark(x0)), nil))
   MARK(add(dbl(x0), x1)) -> c17(MARK(x1))
   MARK(add(first(x0, terms(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, sqr(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   MARK(add(first(x0, dbl(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   MARK(add(first(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2))
   MARK(add(first(x0, recip(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, s(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(x2))
   MARK(add(first(x0, 0), x2)) -> c17(A__ADD(a__first(mark(x0), 0), mark(x2)), MARK(x2))
   MARK(add(first(x0, nil), x2)) -> c17(A__ADD(a__first(mark(x0), nil), mark(x2)), MARK(x2))
   MARK(add(first(terms(z0), x1), x2)) -> c17(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(sqr(z0), x1), x2)) -> c17(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(add(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(dbl(z0), x1), x2)) -> c17(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(first(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(recip(z0), x1), x2)) -> c17(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(s(z0), x1), x2)) -> c17(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(0, x1), x2)) -> c17(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(nil, x1), x2)) -> c17(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(x0, x1), s(z0))) -> c17(A__ADD(a__first(mark(x0), mark(x1)), s(z0)))
   MARK(add(first(x0, x1), 0)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), 0))
   MARK(add(first(x0, x1), nil)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), nil))
   MARK(add(first(x0, x1), x2)) -> c17(MARK(x2))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2


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

(179) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) by 
   MARK(add(terms(z0), s(x1))) -> c17(A__ADD(a__terms(mark(z0)), s(x1)))
   MARK(add(sqr(z0), s(x1))) -> c17(A__ADD(a__sqr(mark(z0)), s(x1)))
   MARK(add(add(z0, z1), s(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), s(x1)))
   MARK(add(dbl(z0), s(x1))) -> c17(A__ADD(a__dbl(mark(z0)), s(x1)))
   MARK(add(first(z0, z1), s(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), s(x1)))
   MARK(add(cons(z0, z1), s(x1))) -> c17(A__ADD(cons(mark(z0), z1), s(x1)))
   MARK(add(recip(z0), s(x1))) -> c17(A__ADD(recip(mark(z0)), s(x1)))
   MARK(add(s(z0), s(x1))) -> c17(A__ADD(s(z0), s(x1)))
   MARK(add(0, s(x1))) -> c17(A__ADD(0, s(x1)))
   MARK(add(nil, s(x1))) -> c17(A__ADD(nil, s(x1)))

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

(180)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
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   MARK(add(nil, s(x1))) -> c17(A__ADD(nil, s(x1)))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2))))
   MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0))
   MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0))
   MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0))
   MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0))
   MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1))))
   MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0))
   MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0))
   MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0))
   MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2))))
   MARK(add(x0, cons(terms(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0))
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   MARK(add(terms(first(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(terms(cons(z0, z1)), x1)) -> c17(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(x1))
   MARK(add(terms(recip(z0)), x1)) -> c17(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(terms(s(z0)), x1)) -> c17(A__ADD(a__terms(s(z0)), mark(x1)), MARK(x1))
   MARK(add(terms(0), x1)) -> c17(A__ADD(a__terms(0), mark(x1)), MARK(x1))
   MARK(add(terms(nil), x1)) -> c17(A__ADD(a__terms(nil), mark(x1)), MARK(x1))
   MARK(add(terms(x0), s(z0))) -> c17(A__ADD(a__terms(mark(x0)), s(z0)))
   MARK(add(terms(x0), 0)) -> c17(A__ADD(a__terms(mark(x0)), 0))
   MARK(add(terms(x0), nil)) -> c17(A__ADD(a__terms(mark(x0)), nil))
   MARK(add(terms(x0), x1)) -> c17(MARK(x1))
   MARK(add(sqr(terms(z0)), x1)) -> c17(A__ADD(a__sqr(a__terms(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(sqr(sqr(z0)), x1)) -> c17(A__ADD(a__sqr(a__sqr(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(sqr(add(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(sqr(dbl(z0)), x1)) -> c17(A__ADD(a__sqr(a__dbl(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(sqr(first(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(sqr(cons(z0, z1)), x1)) -> c17(A__ADD(a__sqr(cons(mark(z0), z1)), mark(x1)), MARK(x1))
   MARK(add(sqr(recip(z0)), x1)) -> c17(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(sqr(s(z0)), x1)) -> c17(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(0), x1)) -> c17(A__ADD(a__sqr(0), mark(x1)), MARK(x1))
   MARK(add(sqr(nil), x1)) -> c17(A__ADD(a__sqr(nil), mark(x1)), MARK(x1))
   MARK(add(sqr(x0), s(z0))) -> c17(A__ADD(a__sqr(mark(x0)), s(z0)))
   MARK(add(sqr(x0), 0)) -> c17(A__ADD(a__sqr(mark(x0)), 0))
   MARK(add(sqr(x0), nil)) -> c17(A__ADD(a__sqr(mark(x0)), nil))
   MARK(add(sqr(x0), x1)) -> c17(MARK(x1))
   MARK(add(add(x0, terms(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(add(x0, sqr(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(add(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   MARK(add(add(x0, dbl(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(add(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   MARK(add(add(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2))
   MARK(add(add(x0, recip(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(add(x0, s(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), s(z0)), mark(x2)), MARK(x2))
   MARK(add(add(x0, 0), x2)) -> c17(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(x2))
   MARK(add(add(x0, nil), x2)) -> c17(A__ADD(a__add(mark(x0), nil), mark(x2)), MARK(x2))
   MARK(add(add(terms(z0), x1), x2)) -> c17(A__ADD(a__add(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(sqr(z0), x1), x2)) -> c17(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(add(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(dbl(z0), x1), x2)) -> c17(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(first(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(recip(z0), x1), x2)) -> c17(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(s(z0), x1), x2)) -> c17(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(0, x1), x2)) -> c17(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(nil, x1), x2)) -> c17(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(x0, x1), s(z0))) -> c17(A__ADD(a__add(mark(x0), mark(x1)), s(z0)))
   MARK(add(add(x0, x1), 0)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), 0))
   MARK(add(add(x0, x1), nil)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), nil))
   MARK(add(add(x0, x1), x2)) -> c17(MARK(x2))
   MARK(add(dbl(terms(z0)), x1)) -> c17(A__ADD(a__dbl(a__terms(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(sqr(z0)), x1)) -> c17(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(add(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(dbl(dbl(z0)), x1)) -> c17(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(first(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(dbl(cons(z0, z1)), x1)) -> c17(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(recip(z0)), x1)) -> c17(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(s(z0)), x1)) -> c17(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(x1))
   MARK(add(dbl(0), x1)) -> c17(A__ADD(a__dbl(0), mark(x1)), MARK(x1))
   MARK(add(dbl(nil), x1)) -> c17(A__ADD(a__dbl(nil), mark(x1)), MARK(x1))
   MARK(add(dbl(x0), s(z0))) -> c17(A__ADD(a__dbl(mark(x0)), s(z0)))
   MARK(add(dbl(x0), 0)) -> c17(A__ADD(a__dbl(mark(x0)), 0))
   MARK(add(dbl(x0), nil)) -> c17(A__ADD(a__dbl(mark(x0)), nil))
   MARK(add(dbl(x0), x1)) -> c17(MARK(x1))
   MARK(add(first(x0, terms(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, sqr(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   MARK(add(first(x0, dbl(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   MARK(add(first(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2))
   MARK(add(first(x0, recip(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, s(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(x2))
   MARK(add(first(x0, 0), x2)) -> c17(A__ADD(a__first(mark(x0), 0), mark(x2)), MARK(x2))
   MARK(add(first(x0, nil), x2)) -> c17(A__ADD(a__first(mark(x0), nil), mark(x2)), MARK(x2))
   MARK(add(first(terms(z0), x1), x2)) -> c17(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(sqr(z0), x1), x2)) -> c17(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(add(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(dbl(z0), x1), x2)) -> c17(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(first(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(recip(z0), x1), x2)) -> c17(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(s(z0), x1), x2)) -> c17(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(0, x1), x2)) -> c17(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(nil, x1), x2)) -> c17(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(x0, x1), s(z0))) -> c17(A__ADD(a__first(mark(x0), mark(x1)), s(z0)))
   MARK(add(first(x0, x1), 0)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), 0))
   MARK(add(first(x0, x1), nil)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), nil))
   MARK(add(first(x0, x1), x2)) -> c17(MARK(x2))
   MARK(add(cons(z0, z1), s(x1))) -> c17(A__ADD(cons(mark(z0), z1), s(x1)))
   MARK(add(recip(z0), s(x1))) -> c17(A__ADD(recip(mark(z0)), s(x1)))
   MARK(add(s(z0), s(x1))) -> c17(A__ADD(s(z0), s(x1)))
   MARK(add(0, s(x1))) -> c17(A__ADD(0, s(x1)))
   MARK(add(nil, s(x1))) -> c17(A__ADD(nil, s(x1)))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2


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

(181) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 4 trailing nodes:
   MARK(add(nil, s(x1))) -> c17(A__ADD(nil, s(x1)))
   MARK(add(recip(z0), s(x1))) -> c17(A__ADD(recip(mark(z0)), s(x1)))
   MARK(add(cons(z0, z1), s(x1))) -> c17(A__ADD(cons(mark(z0), z1), s(x1)))
   MARK(add(s(z0), s(x1))) -> c17(A__ADD(s(z0), s(x1)))

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

(182)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
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   MARK(add(dbl(0), x1)) -> c17(A__ADD(a__dbl(0), mark(x1)), MARK(x1))
   MARK(add(dbl(nil), x1)) -> c17(A__ADD(a__dbl(nil), mark(x1)), MARK(x1))
   MARK(add(dbl(x0), s(z0))) -> c17(A__ADD(a__dbl(mark(x0)), s(z0)))
   MARK(add(dbl(x0), 0)) -> c17(A__ADD(a__dbl(mark(x0)), 0))
   MARK(add(dbl(x0), nil)) -> c17(A__ADD(a__dbl(mark(x0)), nil))
   MARK(add(dbl(x0), x1)) -> c17(MARK(x1))
   MARK(add(first(x0, terms(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, sqr(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   MARK(add(first(x0, dbl(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   MARK(add(first(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2))
   MARK(add(first(x0, recip(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, s(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(x2))
   MARK(add(first(x0, 0), x2)) -> c17(A__ADD(a__first(mark(x0), 0), mark(x2)), MARK(x2))
   MARK(add(first(x0, nil), x2)) -> c17(A__ADD(a__first(mark(x0), nil), mark(x2)), MARK(x2))
   MARK(add(first(terms(z0), x1), x2)) -> c17(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(sqr(z0), x1), x2)) -> c17(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(add(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(dbl(z0), x1), x2)) -> c17(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(first(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(recip(z0), x1), x2)) -> c17(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(s(z0), x1), x2)) -> c17(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(0, x1), x2)) -> c17(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(nil, x1), x2)) -> c17(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(x0, x1), s(z0))) -> c17(A__ADD(a__first(mark(x0), mark(x1)), s(z0)))
   MARK(add(first(x0, x1), 0)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), 0))
   MARK(add(first(x0, x1), nil)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), nil))
   MARK(add(first(x0, x1), x2)) -> c17(MARK(x2))
   MARK(add(0, s(x1))) -> c17(A__ADD(0, s(x1)))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2))))
   MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0))
   MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0))
   MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0))
   MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0))
   MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1))))
   MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0))
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   MARK(add(sqr(z0), cons(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(add(z0, z1), cons(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(dbl(z0), cons(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(first(z0, z1), cons(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(0, cons(x1, x2))) -> c17(A__ADD(0, cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(x0, cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
   MARK(add(cons(z0, z1), cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
   MARK(add(recip(z0), cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
   MARK(add(s(z0), cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
   MARK(add(nil, cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
   MARK(add(x0, recip(terms(z0)))) -> c17(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(recip(terms(z0))))
   MARK(add(x0, recip(sqr(z0)))) -> c17(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(recip(sqr(z0))))
   MARK(add(x0, recip(add(z0, z1)))) -> c17(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(recip(add(z0, z1))))
   MARK(add(x0, recip(dbl(z0)))) -> c17(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(recip(dbl(z0))))
   MARK(add(x0, recip(first(z0, z1)))) -> c17(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(recip(first(z0, z1))))
   MARK(add(x0, recip(cons(z0, z1)))) -> c17(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(recip(cons(z0, z1))))
   MARK(add(x0, recip(recip(z0)))) -> c17(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(recip(recip(z0))))
   MARK(add(x0, recip(s(z0)))) -> c17(A__ADD(mark(x0), recip(s(z0))), MARK(recip(s(z0))))
   MARK(add(x0, recip(0))) -> c17(A__ADD(mark(x0), recip(0)), MARK(recip(0)))
   MARK(add(x0, recip(nil))) -> c17(A__ADD(mark(x0), recip(nil)), MARK(recip(nil)))
   MARK(add(terms(z0), recip(x1))) -> c17(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(sqr(z0), recip(x1))) -> c17(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(add(z0, z1), recip(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(dbl(z0), recip(x1))) -> c17(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(first(z0, z1), recip(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(0, recip(x1))) -> c17(A__ADD(0, recip(mark(x1))), MARK(recip(x1)))
   MARK(add(x0, recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(cons(z0, z1), recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(recip(z0), recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(s(z0), recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(nil, recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(terms(terms(z0)), x1)) -> c17(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(terms(sqr(z0)), x1)) -> c17(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(terms(add(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(terms(dbl(z0)), x1)) -> c17(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(terms(first(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(terms(cons(z0, z1)), x1)) -> c17(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(x1))
   MARK(add(terms(recip(z0)), x1)) -> c17(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(terms(s(z0)), x1)) -> c17(A__ADD(a__terms(s(z0)), mark(x1)), MARK(x1))
   MARK(add(terms(0), x1)) -> c17(A__ADD(a__terms(0), mark(x1)), MARK(x1))
   MARK(add(terms(nil), x1)) -> c17(A__ADD(a__terms(nil), mark(x1)), MARK(x1))
   MARK(add(terms(x0), s(z0))) -> c17(A__ADD(a__terms(mark(x0)), s(z0)))
   MARK(add(terms(x0), 0)) -> c17(A__ADD(a__terms(mark(x0)), 0))
   MARK(add(terms(x0), nil)) -> c17(A__ADD(a__terms(mark(x0)), nil))
   MARK(add(terms(x0), x1)) -> c17(MARK(x1))
   MARK(add(sqr(terms(z0)), x1)) -> c17(A__ADD(a__sqr(a__terms(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(sqr(sqr(z0)), x1)) -> c17(A__ADD(a__sqr(a__sqr(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(sqr(add(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(sqr(dbl(z0)), x1)) -> c17(A__ADD(a__sqr(a__dbl(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(sqr(first(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(sqr(cons(z0, z1)), x1)) -> c17(A__ADD(a__sqr(cons(mark(z0), z1)), mark(x1)), MARK(x1))
   MARK(add(sqr(recip(z0)), x1)) -> c17(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(sqr(s(z0)), x1)) -> c17(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(0), x1)) -> c17(A__ADD(a__sqr(0), mark(x1)), MARK(x1))
   MARK(add(sqr(nil), x1)) -> c17(A__ADD(a__sqr(nil), mark(x1)), MARK(x1))
   MARK(add(sqr(x0), s(z0))) -> c17(A__ADD(a__sqr(mark(x0)), s(z0)))
   MARK(add(sqr(x0), 0)) -> c17(A__ADD(a__sqr(mark(x0)), 0))
   MARK(add(sqr(x0), nil)) -> c17(A__ADD(a__sqr(mark(x0)), nil))
   MARK(add(sqr(x0), x1)) -> c17(MARK(x1))
   MARK(add(add(x0, terms(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(add(x0, sqr(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(add(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   MARK(add(add(x0, dbl(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(add(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   MARK(add(add(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2))
   MARK(add(add(x0, recip(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(add(x0, s(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), s(z0)), mark(x2)), MARK(x2))
   MARK(add(add(x0, 0), x2)) -> c17(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(x2))
   MARK(add(add(x0, nil), x2)) -> c17(A__ADD(a__add(mark(x0), nil), mark(x2)), MARK(x2))
   MARK(add(add(terms(z0), x1), x2)) -> c17(A__ADD(a__add(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(sqr(z0), x1), x2)) -> c17(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(add(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(dbl(z0), x1), x2)) -> c17(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(first(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(recip(z0), x1), x2)) -> c17(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(s(z0), x1), x2)) -> c17(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(0, x1), x2)) -> c17(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(nil, x1), x2)) -> c17(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(x0, x1), s(z0))) -> c17(A__ADD(a__add(mark(x0), mark(x1)), s(z0)))
   MARK(add(add(x0, x1), 0)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), 0))
   MARK(add(add(x0, x1), nil)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), nil))
   MARK(add(add(x0, x1), x2)) -> c17(MARK(x2))
   MARK(add(dbl(terms(z0)), x1)) -> c17(A__ADD(a__dbl(a__terms(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(sqr(z0)), x1)) -> c17(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(add(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(dbl(dbl(z0)), x1)) -> c17(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(first(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(dbl(cons(z0, z1)), x1)) -> c17(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(recip(z0)), x1)) -> c17(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(s(z0)), x1)) -> c17(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(x1))
   MARK(add(dbl(0), x1)) -> c17(A__ADD(a__dbl(0), mark(x1)), MARK(x1))
   MARK(add(dbl(nil), x1)) -> c17(A__ADD(a__dbl(nil), mark(x1)), MARK(x1))
   MARK(add(dbl(x0), s(z0))) -> c17(A__ADD(a__dbl(mark(x0)), s(z0)))
   MARK(add(dbl(x0), 0)) -> c17(A__ADD(a__dbl(mark(x0)), 0))
   MARK(add(dbl(x0), nil)) -> c17(A__ADD(a__dbl(mark(x0)), nil))
   MARK(add(dbl(x0), x1)) -> c17(MARK(x1))
   MARK(add(first(x0, terms(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, sqr(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   MARK(add(first(x0, dbl(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   MARK(add(first(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2))
   MARK(add(first(x0, recip(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, s(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(x2))
   MARK(add(first(x0, 0), x2)) -> c17(A__ADD(a__first(mark(x0), 0), mark(x2)), MARK(x2))
   MARK(add(first(x0, nil), x2)) -> c17(A__ADD(a__first(mark(x0), nil), mark(x2)), MARK(x2))
   MARK(add(first(terms(z0), x1), x2)) -> c17(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(sqr(z0), x1), x2)) -> c17(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(add(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(dbl(z0), x1), x2)) -> c17(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(first(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(recip(z0), x1), x2)) -> c17(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(s(z0), x1), x2)) -> c17(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(0, x1), x2)) -> c17(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(nil, x1), x2)) -> c17(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(x0, x1), s(z0))) -> c17(A__ADD(a__first(mark(x0), mark(x1)), s(z0)))
   MARK(add(first(x0, x1), 0)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), 0))
   MARK(add(first(x0, x1), nil)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), nil))
   MARK(add(first(x0, x1), x2)) -> c17(MARK(x2))
   MARK(add(0, s(x1))) -> c17(A__ADD(0, s(x1)))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2


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

(183) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) by 
   MARK(add(terms(z0), 0)) -> c17(A__ADD(a__terms(mark(z0)), 0))
   MARK(add(sqr(z0), 0)) -> c17(A__ADD(a__sqr(mark(z0)), 0))
   MARK(add(add(z0, z1), 0)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), 0))
   MARK(add(dbl(z0), 0)) -> c17(A__ADD(a__dbl(mark(z0)), 0))
   MARK(add(first(z0, z1), 0)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), 0))
   MARK(add(cons(z0, z1), 0)) -> c17(A__ADD(cons(mark(z0), z1), 0))
   MARK(add(recip(z0), 0)) -> c17(A__ADD(recip(mark(z0)), 0))
   MARK(add(s(z0), 0)) -> c17(A__ADD(s(z0), 0))
   MARK(add(0, 0)) -> c17(A__ADD(0, 0))
   MARK(add(nil, 0)) -> c17(A__ADD(nil, 0))

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

(184)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
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   MARK(add(add(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   MARK(add(add(x0, dbl(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(add(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   MARK(add(add(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2))
   MARK(add(add(x0, recip(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(add(x0, s(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), s(z0)), mark(x2)), MARK(x2))
   MARK(add(add(x0, 0), x2)) -> c17(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(x2))
   MARK(add(add(x0, nil), x2)) -> c17(A__ADD(a__add(mark(x0), nil), mark(x2)), MARK(x2))
   MARK(add(add(terms(z0), x1), x2)) -> c17(A__ADD(a__add(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(sqr(z0), x1), x2)) -> c17(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(add(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(dbl(z0), x1), x2)) -> c17(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(first(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(recip(z0), x1), x2)) -> c17(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(s(z0), x1), x2)) -> c17(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(0, x1), x2)) -> c17(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(nil, x1), x2)) -> c17(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(x0, x1), s(z0))) -> c17(A__ADD(a__add(mark(x0), mark(x1)), s(z0)))
   MARK(add(add(x0, x1), 0)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), 0))
   MARK(add(add(x0, x1), nil)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), nil))
   MARK(add(add(x0, x1), x2)) -> c17(MARK(x2))
   MARK(add(dbl(terms(z0)), x1)) -> c17(A__ADD(a__dbl(a__terms(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(sqr(z0)), x1)) -> c17(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(add(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(dbl(dbl(z0)), x1)) -> c17(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(first(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(dbl(cons(z0, z1)), x1)) -> c17(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(recip(z0)), x1)) -> c17(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(s(z0)), x1)) -> c17(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(x1))
   MARK(add(dbl(0), x1)) -> c17(A__ADD(a__dbl(0), mark(x1)), MARK(x1))
   MARK(add(dbl(nil), x1)) -> c17(A__ADD(a__dbl(nil), mark(x1)), MARK(x1))
   MARK(add(dbl(x0), s(z0))) -> c17(A__ADD(a__dbl(mark(x0)), s(z0)))
   MARK(add(dbl(x0), 0)) -> c17(A__ADD(a__dbl(mark(x0)), 0))
   MARK(add(dbl(x0), nil)) -> c17(A__ADD(a__dbl(mark(x0)), nil))
   MARK(add(dbl(x0), x1)) -> c17(MARK(x1))
   MARK(add(first(x0, terms(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, sqr(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   MARK(add(first(x0, dbl(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   MARK(add(first(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2))
   MARK(add(first(x0, recip(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, s(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(x2))
   MARK(add(first(x0, 0), x2)) -> c17(A__ADD(a__first(mark(x0), 0), mark(x2)), MARK(x2))
   MARK(add(first(x0, nil), x2)) -> c17(A__ADD(a__first(mark(x0), nil), mark(x2)), MARK(x2))
   MARK(add(first(terms(z0), x1), x2)) -> c17(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(sqr(z0), x1), x2)) -> c17(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(add(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(dbl(z0), x1), x2)) -> c17(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(first(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(recip(z0), x1), x2)) -> c17(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(s(z0), x1), x2)) -> c17(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(0, x1), x2)) -> c17(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(nil, x1), x2)) -> c17(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(x0, x1), s(z0))) -> c17(A__ADD(a__first(mark(x0), mark(x1)), s(z0)))
   MARK(add(first(x0, x1), 0)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), 0))
   MARK(add(first(x0, x1), nil)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), nil))
   MARK(add(first(x0, x1), x2)) -> c17(MARK(x2))
   MARK(add(0, s(x1))) -> c17(A__ADD(0, s(x1)))
   MARK(add(cons(z0, z1), 0)) -> c17(A__ADD(cons(mark(z0), z1), 0))
   MARK(add(recip(z0), 0)) -> c17(A__ADD(recip(mark(z0)), 0))
   MARK(add(s(z0), 0)) -> c17(A__ADD(s(z0), 0))
   MARK(add(0, 0)) -> c17(A__ADD(0, 0))
   MARK(add(nil, 0)) -> c17(A__ADD(nil, 0))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
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   MARK(add(x0, recip(s(z0)))) -> c17(A__ADD(mark(x0), recip(s(z0))), MARK(recip(s(z0))))
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   MARK(add(s(z0), recip(x1))) -> c17(MARK(recip(x1)))
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   MARK(add(sqr(sqr(z0)), x1)) -> c17(A__ADD(a__sqr(a__sqr(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(sqr(add(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1))
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   MARK(add(sqr(x0), s(z0))) -> c17(A__ADD(a__sqr(mark(x0)), s(z0)))
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   MARK(add(add(terms(z0), x1), x2)) -> c17(A__ADD(a__add(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
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   MARK(add(dbl(cons(z0, z1)), x1)) -> c17(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(recip(z0)), x1)) -> c17(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(x1))
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   MARK(add(first(x0, s(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(x2))
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   MARK(add(first(add(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
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   MARK(add(first(recip(z0), x1), x2)) -> c17(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(s(z0), x1), x2)) -> c17(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(0, x1), x2)) -> c17(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(x2))
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   MARK(add(first(x0, x1), 0)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), 0))
   MARK(add(first(x0, x1), nil)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), nil))
   MARK(add(first(x0, x1), x2)) -> c17(MARK(x2))
   MARK(add(0, s(x1))) -> c17(A__ADD(0, s(x1)))
   MARK(add(cons(z0, z1), 0)) -> c17(A__ADD(cons(mark(z0), z1), 0))
   MARK(add(recip(z0), 0)) -> c17(A__ADD(recip(mark(z0)), 0))
   MARK(add(s(z0), 0)) -> c17(A__ADD(s(z0), 0))
   MARK(add(0, 0)) -> c17(A__ADD(0, 0))
   MARK(add(nil, 0)) -> c17(A__ADD(nil, 0))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2


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

(185) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 4 trailing nodes:
   MARK(add(s(z0), 0)) -> c17(A__ADD(s(z0), 0))
   MARK(add(recip(z0), 0)) -> c17(A__ADD(recip(mark(z0)), 0))
   MARK(add(cons(z0, z1), 0)) -> c17(A__ADD(cons(mark(z0), z1), 0))
   MARK(add(nil, 0)) -> c17(A__ADD(nil, 0))

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

(186)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2))))
   MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0))
   MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0))
   MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0))
   MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0))
   MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1))))
   MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0))
   MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0))
   MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0))
   MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0)))
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   MARK(add(first(z0, z1), recip(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(0, recip(x1))) -> c17(A__ADD(0, recip(mark(x1))), MARK(recip(x1)))
   MARK(add(x0, recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(cons(z0, z1), recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(recip(z0), recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(s(z0), recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(nil, recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(terms(terms(z0)), x1)) -> c17(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(terms(sqr(z0)), x1)) -> c17(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(terms(add(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(terms(dbl(z0)), x1)) -> c17(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(terms(first(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(terms(cons(z0, z1)), x1)) -> c17(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(x1))
   MARK(add(terms(recip(z0)), x1)) -> c17(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(terms(s(z0)), x1)) -> c17(A__ADD(a__terms(s(z0)), mark(x1)), MARK(x1))
   MARK(add(terms(0), x1)) -> c17(A__ADD(a__terms(0), mark(x1)), MARK(x1))
   MARK(add(terms(nil), x1)) -> c17(A__ADD(a__terms(nil), mark(x1)), MARK(x1))
   MARK(add(terms(x0), s(z0))) -> c17(A__ADD(a__terms(mark(x0)), s(z0)))
   MARK(add(terms(x0), 0)) -> c17(A__ADD(a__terms(mark(x0)), 0))
   MARK(add(terms(x0), nil)) -> c17(A__ADD(a__terms(mark(x0)), nil))
   MARK(add(terms(x0), x1)) -> c17(MARK(x1))
   MARK(add(sqr(terms(z0)), x1)) -> c17(A__ADD(a__sqr(a__terms(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(sqr(sqr(z0)), x1)) -> c17(A__ADD(a__sqr(a__sqr(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(sqr(add(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(sqr(dbl(z0)), x1)) -> c17(A__ADD(a__sqr(a__dbl(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(sqr(first(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(sqr(cons(z0, z1)), x1)) -> c17(A__ADD(a__sqr(cons(mark(z0), z1)), mark(x1)), MARK(x1))
   MARK(add(sqr(recip(z0)), x1)) -> c17(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(sqr(s(z0)), x1)) -> c17(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(0), x1)) -> c17(A__ADD(a__sqr(0), mark(x1)), MARK(x1))
   MARK(add(sqr(nil), x1)) -> c17(A__ADD(a__sqr(nil), mark(x1)), MARK(x1))
   MARK(add(sqr(x0), s(z0))) -> c17(A__ADD(a__sqr(mark(x0)), s(z0)))
   MARK(add(sqr(x0), 0)) -> c17(A__ADD(a__sqr(mark(x0)), 0))
   MARK(add(sqr(x0), nil)) -> c17(A__ADD(a__sqr(mark(x0)), nil))
   MARK(add(sqr(x0), x1)) -> c17(MARK(x1))
   MARK(add(add(x0, terms(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(add(x0, sqr(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(add(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   MARK(add(add(x0, dbl(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(add(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   MARK(add(add(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2))
   MARK(add(add(x0, recip(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(add(x0, s(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), s(z0)), mark(x2)), MARK(x2))
   MARK(add(add(x0, 0), x2)) -> c17(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(x2))
   MARK(add(add(x0, nil), x2)) -> c17(A__ADD(a__add(mark(x0), nil), mark(x2)), MARK(x2))
   MARK(add(add(terms(z0), x1), x2)) -> c17(A__ADD(a__add(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(sqr(z0), x1), x2)) -> c17(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(add(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(dbl(z0), x1), x2)) -> c17(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(first(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(recip(z0), x1), x2)) -> c17(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(s(z0), x1), x2)) -> c17(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(0, x1), x2)) -> c17(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(nil, x1), x2)) -> c17(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(x0, x1), s(z0))) -> c17(A__ADD(a__add(mark(x0), mark(x1)), s(z0)))
   MARK(add(add(x0, x1), 0)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), 0))
   MARK(add(add(x0, x1), nil)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), nil))
   MARK(add(add(x0, x1), x2)) -> c17(MARK(x2))
   MARK(add(dbl(terms(z0)), x1)) -> c17(A__ADD(a__dbl(a__terms(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(sqr(z0)), x1)) -> c17(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(add(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(dbl(dbl(z0)), x1)) -> c17(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(first(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(dbl(cons(z0, z1)), x1)) -> c17(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(recip(z0)), x1)) -> c17(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(s(z0)), x1)) -> c17(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(x1))
   MARK(add(dbl(0), x1)) -> c17(A__ADD(a__dbl(0), mark(x1)), MARK(x1))
   MARK(add(dbl(nil), x1)) -> c17(A__ADD(a__dbl(nil), mark(x1)), MARK(x1))
   MARK(add(dbl(x0), s(z0))) -> c17(A__ADD(a__dbl(mark(x0)), s(z0)))
   MARK(add(dbl(x0), 0)) -> c17(A__ADD(a__dbl(mark(x0)), 0))
   MARK(add(dbl(x0), nil)) -> c17(A__ADD(a__dbl(mark(x0)), nil))
   MARK(add(dbl(x0), x1)) -> c17(MARK(x1))
   MARK(add(first(x0, terms(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, sqr(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   MARK(add(first(x0, dbl(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   MARK(add(first(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2))
   MARK(add(first(x0, recip(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, s(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(x2))
   MARK(add(first(x0, 0), x2)) -> c17(A__ADD(a__first(mark(x0), 0), mark(x2)), MARK(x2))
   MARK(add(first(x0, nil), x2)) -> c17(A__ADD(a__first(mark(x0), nil), mark(x2)), MARK(x2))
   MARK(add(first(terms(z0), x1), x2)) -> c17(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(sqr(z0), x1), x2)) -> c17(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(add(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(dbl(z0), x1), x2)) -> c17(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(first(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(recip(z0), x1), x2)) -> c17(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(s(z0), x1), x2)) -> c17(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(0, x1), x2)) -> c17(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(nil, x1), x2)) -> c17(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(x0, x1), s(z0))) -> c17(A__ADD(a__first(mark(x0), mark(x1)), s(z0)))
   MARK(add(first(x0, x1), 0)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), 0))
   MARK(add(first(x0, x1), nil)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), nil))
   MARK(add(first(x0, x1), x2)) -> c17(MARK(x2))
   MARK(add(0, s(x1))) -> c17(A__ADD(0, s(x1)))
   MARK(add(0, 0)) -> c17(A__ADD(0, 0))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
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   MARK(add(first(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2))
   MARK(add(first(x0, recip(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, s(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(x2))
   MARK(add(first(x0, 0), x2)) -> c17(A__ADD(a__first(mark(x0), 0), mark(x2)), MARK(x2))
   MARK(add(first(x0, nil), x2)) -> c17(A__ADD(a__first(mark(x0), nil), mark(x2)), MARK(x2))
   MARK(add(first(terms(z0), x1), x2)) -> c17(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(sqr(z0), x1), x2)) -> c17(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(add(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(dbl(z0), x1), x2)) -> c17(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(first(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(recip(z0), x1), x2)) -> c17(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(s(z0), x1), x2)) -> c17(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(0, x1), x2)) -> c17(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(nil, x1), x2)) -> c17(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(x0, x1), s(z0))) -> c17(A__ADD(a__first(mark(x0), mark(x1)), s(z0)))
   MARK(add(first(x0, x1), 0)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), 0))
   MARK(add(first(x0, x1), nil)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), nil))
   MARK(add(first(x0, x1), x2)) -> c17(MARK(x2))
   MARK(add(0, s(x1))) -> c17(A__ADD(0, s(x1)))
   MARK(add(0, 0)) -> c17(A__ADD(0, 0))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2


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

(187) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) by 
   MARK(add(terms(z0), nil)) -> c17(A__ADD(a__terms(mark(z0)), nil))
   MARK(add(sqr(z0), nil)) -> c17(A__ADD(a__sqr(mark(z0)), nil))
   MARK(add(add(z0, z1), nil)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), nil))
   MARK(add(dbl(z0), nil)) -> c17(A__ADD(a__dbl(mark(z0)), nil))
   MARK(add(first(z0, z1), nil)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), nil))
   MARK(add(cons(z0, z1), nil)) -> c17(A__ADD(cons(mark(z0), z1), nil))
   MARK(add(recip(z0), nil)) -> c17(A__ADD(recip(mark(z0)), nil))
   MARK(add(s(z0), nil)) -> c17(A__ADD(s(z0), nil))
   MARK(add(0, nil)) -> c17(A__ADD(0, nil))
   MARK(add(nil, nil)) -> c17(A__ADD(nil, nil))

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

(188)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2))))
   MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0))
   MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0))
   MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0))
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   MARK(add(s(z0), recip(x1))) -> c17(MARK(recip(x1)))
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   MARK(add(terms(cons(z0, z1)), x1)) -> c17(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(x1))
   MARK(add(terms(recip(z0)), x1)) -> c17(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(terms(s(z0)), x1)) -> c17(A__ADD(a__terms(s(z0)), mark(x1)), MARK(x1))
   MARK(add(terms(0), x1)) -> c17(A__ADD(a__terms(0), mark(x1)), MARK(x1))
   MARK(add(terms(nil), x1)) -> c17(A__ADD(a__terms(nil), mark(x1)), MARK(x1))
   MARK(add(terms(x0), s(z0))) -> c17(A__ADD(a__terms(mark(x0)), s(z0)))
   MARK(add(terms(x0), 0)) -> c17(A__ADD(a__terms(mark(x0)), 0))
   MARK(add(terms(x0), nil)) -> c17(A__ADD(a__terms(mark(x0)), nil))
   MARK(add(terms(x0), x1)) -> c17(MARK(x1))
   MARK(add(sqr(terms(z0)), x1)) -> c17(A__ADD(a__sqr(a__terms(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(sqr(sqr(z0)), x1)) -> c17(A__ADD(a__sqr(a__sqr(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(sqr(add(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(sqr(dbl(z0)), x1)) -> c17(A__ADD(a__sqr(a__dbl(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(sqr(first(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1))
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   MARK(add(sqr(nil), x1)) -> c17(A__ADD(a__sqr(nil), mark(x1)), MARK(x1))
   MARK(add(sqr(x0), s(z0))) -> c17(A__ADD(a__sqr(mark(x0)), s(z0)))
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   MARK(add(add(x0, s(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), s(z0)), mark(x2)), MARK(x2))
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   MARK(add(dbl(cons(z0, z1)), x1)) -> c17(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(recip(z0)), x1)) -> c17(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(s(z0)), x1)) -> c17(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(x1))
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   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
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   MARK(add(s(z0), x1)) -> c17(MARK(x1))
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   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
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   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
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   MARK(add(add(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2))
   MARK(add(add(x0, recip(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(add(x0, s(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), s(z0)), mark(x2)), MARK(x2))
   MARK(add(add(x0, 0), x2)) -> c17(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(x2))
   MARK(add(add(x0, nil), x2)) -> c17(A__ADD(a__add(mark(x0), nil), mark(x2)), MARK(x2))
   MARK(add(add(terms(z0), x1), x2)) -> c17(A__ADD(a__add(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(sqr(z0), x1), x2)) -> c17(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(add(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(dbl(z0), x1), x2)) -> c17(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(first(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(recip(z0), x1), x2)) -> c17(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(s(z0), x1), x2)) -> c17(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(0, x1), x2)) -> c17(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(nil, x1), x2)) -> c17(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(x0, x1), s(z0))) -> c17(A__ADD(a__add(mark(x0), mark(x1)), s(z0)))
   MARK(add(add(x0, x1), 0)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), 0))
   MARK(add(add(x0, x1), nil)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), nil))
   MARK(add(add(x0, x1), x2)) -> c17(MARK(x2))
   MARK(add(dbl(terms(z0)), x1)) -> c17(A__ADD(a__dbl(a__terms(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(sqr(z0)), x1)) -> c17(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(add(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(dbl(dbl(z0)), x1)) -> c17(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(first(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(dbl(cons(z0, z1)), x1)) -> c17(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(recip(z0)), x1)) -> c17(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(s(z0)), x1)) -> c17(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(x1))
   MARK(add(dbl(0), x1)) -> c17(A__ADD(a__dbl(0), mark(x1)), MARK(x1))
   MARK(add(dbl(nil), x1)) -> c17(A__ADD(a__dbl(nil), mark(x1)), MARK(x1))
   MARK(add(dbl(x0), s(z0))) -> c17(A__ADD(a__dbl(mark(x0)), s(z0)))
   MARK(add(dbl(x0), 0)) -> c17(A__ADD(a__dbl(mark(x0)), 0))
   MARK(add(dbl(x0), nil)) -> c17(A__ADD(a__dbl(mark(x0)), nil))
   MARK(add(dbl(x0), x1)) -> c17(MARK(x1))
   MARK(add(first(x0, terms(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, sqr(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   MARK(add(first(x0, dbl(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   MARK(add(first(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2))
   MARK(add(first(x0, recip(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, s(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(x2))
   MARK(add(first(x0, 0), x2)) -> c17(A__ADD(a__first(mark(x0), 0), mark(x2)), MARK(x2))
   MARK(add(first(x0, nil), x2)) -> c17(A__ADD(a__first(mark(x0), nil), mark(x2)), MARK(x2))
   MARK(add(first(terms(z0), x1), x2)) -> c17(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(sqr(z0), x1), x2)) -> c17(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(add(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(dbl(z0), x1), x2)) -> c17(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(first(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(recip(z0), x1), x2)) -> c17(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(s(z0), x1), x2)) -> c17(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(0, x1), x2)) -> c17(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(nil, x1), x2)) -> c17(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(x0, x1), s(z0))) -> c17(A__ADD(a__first(mark(x0), mark(x1)), s(z0)))
   MARK(add(first(x0, x1), 0)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), 0))
   MARK(add(first(x0, x1), nil)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), nil))
   MARK(add(first(x0, x1), x2)) -> c17(MARK(x2))
   MARK(add(0, s(x1))) -> c17(A__ADD(0, s(x1)))
   MARK(add(0, 0)) -> c17(A__ADD(0, 0))
   MARK(add(cons(z0, z1), nil)) -> c17(A__ADD(cons(mark(z0), z1), nil))
   MARK(add(recip(z0), nil)) -> c17(A__ADD(recip(mark(z0)), nil))
   MARK(add(s(z0), nil)) -> c17(A__ADD(s(z0), nil))
   MARK(add(0, nil)) -> c17(A__ADD(0, nil))
   MARK(add(nil, nil)) -> c17(A__ADD(nil, nil))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2


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

(189) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 4 trailing nodes:
   MARK(add(cons(z0, z1), nil)) -> c17(A__ADD(cons(mark(z0), z1), nil))
   MARK(add(s(z0), nil)) -> c17(A__ADD(s(z0), nil))
   MARK(add(nil, nil)) -> c17(A__ADD(nil, nil))
   MARK(add(recip(z0), nil)) -> c17(A__ADD(recip(mark(z0)), nil))

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

(190)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
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   MARK(add(first(nil, x1), x2)) -> c17(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(x0, x1), s(z0))) -> c17(A__ADD(a__first(mark(x0), mark(x1)), s(z0)))
   MARK(add(first(x0, x1), 0)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), 0))
   MARK(add(first(x0, x1), nil)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), nil))
   MARK(add(first(x0, x1), x2)) -> c17(MARK(x2))
   MARK(add(0, s(x1))) -> c17(A__ADD(0, s(x1)))
   MARK(add(0, 0)) -> c17(A__ADD(0, 0))
   MARK(add(0, nil)) -> c17(A__ADD(0, nil))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2))))
   MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0))
   MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0))
   MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0))
   MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0))
   MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1))))
   MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0))
   MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0))
   MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0))
   MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0)))
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   MARK(add(s(z0), recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(nil, recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(terms(terms(z0)), x1)) -> c17(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(terms(sqr(z0)), x1)) -> c17(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(terms(add(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(terms(dbl(z0)), x1)) -> c17(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(terms(first(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(terms(cons(z0, z1)), x1)) -> c17(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(x1))
   MARK(add(terms(recip(z0)), x1)) -> c17(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(terms(s(z0)), x1)) -> c17(A__ADD(a__terms(s(z0)), mark(x1)), MARK(x1))
   MARK(add(terms(0), x1)) -> c17(A__ADD(a__terms(0), mark(x1)), MARK(x1))
   MARK(add(terms(nil), x1)) -> c17(A__ADD(a__terms(nil), mark(x1)), MARK(x1))
   MARK(add(terms(x0), s(z0))) -> c17(A__ADD(a__terms(mark(x0)), s(z0)))
   MARK(add(terms(x0), 0)) -> c17(A__ADD(a__terms(mark(x0)), 0))
   MARK(add(terms(x0), nil)) -> c17(A__ADD(a__terms(mark(x0)), nil))
   MARK(add(terms(x0), x1)) -> c17(MARK(x1))
   MARK(add(sqr(terms(z0)), x1)) -> c17(A__ADD(a__sqr(a__terms(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(sqr(sqr(z0)), x1)) -> c17(A__ADD(a__sqr(a__sqr(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(sqr(add(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(sqr(dbl(z0)), x1)) -> c17(A__ADD(a__sqr(a__dbl(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(sqr(first(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(sqr(cons(z0, z1)), x1)) -> c17(A__ADD(a__sqr(cons(mark(z0), z1)), mark(x1)), MARK(x1))
   MARK(add(sqr(recip(z0)), x1)) -> c17(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(sqr(s(z0)), x1)) -> c17(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(0), x1)) -> c17(A__ADD(a__sqr(0), mark(x1)), MARK(x1))
   MARK(add(sqr(nil), x1)) -> c17(A__ADD(a__sqr(nil), mark(x1)), MARK(x1))
   MARK(add(sqr(x0), s(z0))) -> c17(A__ADD(a__sqr(mark(x0)), s(z0)))
   MARK(add(sqr(x0), 0)) -> c17(A__ADD(a__sqr(mark(x0)), 0))
   MARK(add(sqr(x0), nil)) -> c17(A__ADD(a__sqr(mark(x0)), nil))
   MARK(add(sqr(x0), x1)) -> c17(MARK(x1))
   MARK(add(add(x0, terms(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(add(x0, sqr(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(add(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   MARK(add(add(x0, dbl(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(add(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   MARK(add(add(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2))
   MARK(add(add(x0, recip(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(add(x0, s(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), s(z0)), mark(x2)), MARK(x2))
   MARK(add(add(x0, 0), x2)) -> c17(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(x2))
   MARK(add(add(x0, nil), x2)) -> c17(A__ADD(a__add(mark(x0), nil), mark(x2)), MARK(x2))
   MARK(add(add(terms(z0), x1), x2)) -> c17(A__ADD(a__add(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(sqr(z0), x1), x2)) -> c17(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(add(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(dbl(z0), x1), x2)) -> c17(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(first(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(recip(z0), x1), x2)) -> c17(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(s(z0), x1), x2)) -> c17(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(0, x1), x2)) -> c17(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(nil, x1), x2)) -> c17(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(x0, x1), s(z0))) -> c17(A__ADD(a__add(mark(x0), mark(x1)), s(z0)))
   MARK(add(add(x0, x1), 0)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), 0))
   MARK(add(add(x0, x1), nil)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), nil))
   MARK(add(add(x0, x1), x2)) -> c17(MARK(x2))
   MARK(add(dbl(terms(z0)), x1)) -> c17(A__ADD(a__dbl(a__terms(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(sqr(z0)), x1)) -> c17(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(add(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(dbl(dbl(z0)), x1)) -> c17(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(first(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(dbl(cons(z0, z1)), x1)) -> c17(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(recip(z0)), x1)) -> c17(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(s(z0)), x1)) -> c17(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(x1))
   MARK(add(dbl(0), x1)) -> c17(A__ADD(a__dbl(0), mark(x1)), MARK(x1))
   MARK(add(dbl(nil), x1)) -> c17(A__ADD(a__dbl(nil), mark(x1)), MARK(x1))
   MARK(add(dbl(x0), s(z0))) -> c17(A__ADD(a__dbl(mark(x0)), s(z0)))
   MARK(add(dbl(x0), 0)) -> c17(A__ADD(a__dbl(mark(x0)), 0))
   MARK(add(dbl(x0), nil)) -> c17(A__ADD(a__dbl(mark(x0)), nil))
   MARK(add(dbl(x0), x1)) -> c17(MARK(x1))
   MARK(add(first(x0, terms(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, sqr(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   MARK(add(first(x0, dbl(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   MARK(add(first(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2))
   MARK(add(first(x0, recip(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, s(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(x2))
   MARK(add(first(x0, 0), x2)) -> c17(A__ADD(a__first(mark(x0), 0), mark(x2)), MARK(x2))
   MARK(add(first(x0, nil), x2)) -> c17(A__ADD(a__first(mark(x0), nil), mark(x2)), MARK(x2))
   MARK(add(first(terms(z0), x1), x2)) -> c17(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(sqr(z0), x1), x2)) -> c17(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(add(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(dbl(z0), x1), x2)) -> c17(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(first(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(recip(z0), x1), x2)) -> c17(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(s(z0), x1), x2)) -> c17(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(0, x1), x2)) -> c17(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(nil, x1), x2)) -> c17(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(x0, x1), s(z0))) -> c17(A__ADD(a__first(mark(x0), mark(x1)), s(z0)))
   MARK(add(first(x0, x1), 0)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), 0))
   MARK(add(first(x0, x1), nil)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), nil))
   MARK(add(first(x0, x1), x2)) -> c17(MARK(x2))
   MARK(add(0, s(x1))) -> c17(A__ADD(0, s(x1)))
   MARK(add(0, 0)) -> c17(A__ADD(0, 0))
   MARK(add(0, nil)) -> c17(A__ADD(0, nil))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2


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

(191) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) by 
   MARK(first(x0, terms(x1))) -> c19(A__FIRST(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(first(x0, terms(x1))) -> c19(A__FIRST(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(first(x0, terms(terms(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(first(x0, terms(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(first(x0, terms(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, terms(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(first(x0, terms(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, terms(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(first(x0, terms(recip(z0)))) -> c19(A__FIRST(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(first(x0, terms(s(z0)))) -> c19(A__FIRST(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(first(x0, terms(0))) -> c19(A__FIRST(mark(x0), a__terms(0)), MARK(x0))
   MARK(first(x0, terms(nil))) -> c19(A__FIRST(mark(x0), a__terms(nil)), MARK(x0))
   MARK(first(terms(z0), terms(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(first(sqr(z0), terms(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(first(add(z0, z1), terms(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(first(dbl(z0), terms(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(first(first(z0, z1), terms(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(first(cons(z0, z1), terms(x1))) -> c19(A__FIRST(cons(mark(z0), z1), a__terms(mark(x1))), MARK(cons(z0, z1)))
   MARK(first(recip(z0), terms(x1))) -> c19(A__FIRST(recip(mark(z0)), a__terms(mark(x1))), MARK(recip(z0)))
   MARK(first(s(z0), terms(x1))) -> c19(A__FIRST(s(z0), a__terms(mark(x1))), MARK(s(z0)))
   MARK(first(0, terms(x1))) -> c19(A__FIRST(0, a__terms(mark(x1))), MARK(0))
   MARK(first(nil, terms(x1))) -> c19(A__FIRST(nil, a__terms(mark(x1))), MARK(nil))

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

(192)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
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   MARK(add(add(dbl(z0), x1), x2)) -> c17(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(first(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(recip(z0), x1), x2)) -> c17(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(s(z0), x1), x2)) -> c17(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(0, x1), x2)) -> c17(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(nil, x1), x2)) -> c17(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(x0, x1), s(z0))) -> c17(A__ADD(a__add(mark(x0), mark(x1)), s(z0)))
   MARK(add(add(x0, x1), 0)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), 0))
   MARK(add(add(x0, x1), nil)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), nil))
   MARK(add(add(x0, x1), x2)) -> c17(MARK(x2))
   MARK(add(dbl(terms(z0)), x1)) -> c17(A__ADD(a__dbl(a__terms(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(sqr(z0)), x1)) -> c17(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(add(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(dbl(dbl(z0)), x1)) -> c17(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(first(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(dbl(cons(z0, z1)), x1)) -> c17(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(recip(z0)), x1)) -> c17(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(s(z0)), x1)) -> c17(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(x1))
   MARK(add(dbl(0), x1)) -> c17(A__ADD(a__dbl(0), mark(x1)), MARK(x1))
   MARK(add(dbl(nil), x1)) -> c17(A__ADD(a__dbl(nil), mark(x1)), MARK(x1))
   MARK(add(dbl(x0), s(z0))) -> c17(A__ADD(a__dbl(mark(x0)), s(z0)))
   MARK(add(dbl(x0), 0)) -> c17(A__ADD(a__dbl(mark(x0)), 0))
   MARK(add(dbl(x0), nil)) -> c17(A__ADD(a__dbl(mark(x0)), nil))
   MARK(add(dbl(x0), x1)) -> c17(MARK(x1))
   MARK(add(first(x0, terms(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, sqr(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   MARK(add(first(x0, dbl(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   MARK(add(first(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2))
   MARK(add(first(x0, recip(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, s(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(x2))
   MARK(add(first(x0, 0), x2)) -> c17(A__ADD(a__first(mark(x0), 0), mark(x2)), MARK(x2))
   MARK(add(first(x0, nil), x2)) -> c17(A__ADD(a__first(mark(x0), nil), mark(x2)), MARK(x2))
   MARK(add(first(terms(z0), x1), x2)) -> c17(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(sqr(z0), x1), x2)) -> c17(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(add(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(dbl(z0), x1), x2)) -> c17(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(first(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(recip(z0), x1), x2)) -> c17(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(s(z0), x1), x2)) -> c17(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(0, x1), x2)) -> c17(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(nil, x1), x2)) -> c17(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(x0, x1), s(z0))) -> c17(A__ADD(a__first(mark(x0), mark(x1)), s(z0)))
   MARK(add(first(x0, x1), 0)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), 0))
   MARK(add(first(x0, x1), nil)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), nil))
   MARK(add(first(x0, x1), x2)) -> c17(MARK(x2))
   MARK(add(0, s(x1))) -> c17(A__ADD(0, s(x1)))
   MARK(add(0, 0)) -> c17(A__ADD(0, 0))
   MARK(add(0, nil)) -> c17(A__ADD(0, nil))
   MARK(first(x0, terms(x1))) -> c19(A__FIRST(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(first(x0, terms(x1))) -> c19(A__FIRST(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(first(x0, terms(terms(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(first(x0, terms(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(first(x0, terms(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, terms(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(first(x0, terms(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, terms(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(first(x0, terms(recip(z0)))) -> c19(A__FIRST(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(first(x0, terms(s(z0)))) -> c19(A__FIRST(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(first(x0, terms(0))) -> c19(A__FIRST(mark(x0), a__terms(0)), MARK(x0))
   MARK(first(x0, terms(nil))) -> c19(A__FIRST(mark(x0), a__terms(nil)), MARK(x0))
   MARK(first(terms(z0), terms(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(first(sqr(z0), terms(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(first(add(z0, z1), terms(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(first(dbl(z0), terms(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(first(first(z0, z1), terms(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(first(cons(z0, z1), terms(x1))) -> c19(A__FIRST(cons(mark(z0), z1), a__terms(mark(x1))), MARK(cons(z0, z1)))
   MARK(first(recip(z0), terms(x1))) -> c19(A__FIRST(recip(mark(z0)), a__terms(mark(x1))), MARK(recip(z0)))
   MARK(first(s(z0), terms(x1))) -> c19(A__FIRST(s(z0), a__terms(mark(x1))), MARK(s(z0)))
   MARK(first(0, terms(x1))) -> c19(A__FIRST(0, a__terms(mark(x1))), MARK(0))
   MARK(first(nil, terms(x1))) -> c19(A__FIRST(nil, a__terms(mark(x1))), MARK(nil))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
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   MARK(first(x0, terms(x1))) -> c19(A__FIRST(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(first(x0, terms(terms(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(first(x0, terms(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(first(x0, terms(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, terms(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(first(x0, terms(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, terms(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(first(x0, terms(recip(z0)))) -> c19(A__FIRST(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(first(x0, terms(s(z0)))) -> c19(A__FIRST(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(first(x0, terms(0))) -> c19(A__FIRST(mark(x0), a__terms(0)), MARK(x0))
   MARK(first(x0, terms(nil))) -> c19(A__FIRST(mark(x0), a__terms(nil)), MARK(x0))
   MARK(first(terms(z0), terms(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(first(sqr(z0), terms(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(first(add(z0, z1), terms(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(first(dbl(z0), terms(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(first(first(z0, z1), terms(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(first(cons(z0, z1), terms(x1))) -> c19(A__FIRST(cons(mark(z0), z1), a__terms(mark(x1))), MARK(cons(z0, z1)))
   MARK(first(recip(z0), terms(x1))) -> c19(A__FIRST(recip(mark(z0)), a__terms(mark(x1))), MARK(recip(z0)))
   MARK(first(s(z0), terms(x1))) -> c19(A__FIRST(s(z0), a__terms(mark(x1))), MARK(s(z0)))
   MARK(first(0, terms(x1))) -> c19(A__FIRST(0, a__terms(mark(x1))), MARK(0))
   MARK(first(nil, terms(x1))) -> c19(A__FIRST(nil, a__terms(mark(x1))), MARK(nil))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2


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

(193) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing nodes:
   MARK(first(0, terms(x1))) -> c19(A__FIRST(0, a__terms(mark(x1))), MARK(0))
   MARK(first(nil, terms(x1))) -> c19(A__FIRST(nil, a__terms(mark(x1))), MARK(nil))

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

(194)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2))))
   MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0))
   MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0))
   MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0))
   MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0))
   MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1)))
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   MARK(add(0, recip(x1))) -> c17(A__ADD(0, recip(mark(x1))), MARK(recip(x1)))
   MARK(add(x0, recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(cons(z0, z1), recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(recip(z0), recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(s(z0), recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(nil, recip(x1))) -> c17(MARK(recip(x1)))
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   MARK(add(terms(sqr(z0)), x1)) -> c17(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(x1))
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   MARK(add(terms(dbl(z0)), x1)) -> c17(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(x1))
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   MARK(add(terms(cons(z0, z1)), x1)) -> c17(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(x1))
   MARK(add(terms(recip(z0)), x1)) -> c17(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(terms(s(z0)), x1)) -> c17(A__ADD(a__terms(s(z0)), mark(x1)), MARK(x1))
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   MARK(add(sqr(dbl(z0)), x1)) -> c17(A__ADD(a__sqr(a__dbl(mark(z0))), mark(x1)), MARK(x1))
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   MARK(add(sqr(cons(z0, z1)), x1)) -> c17(A__ADD(a__sqr(cons(mark(z0), z1)), mark(x1)), MARK(x1))
   MARK(add(sqr(recip(z0)), x1)) -> c17(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(sqr(s(z0)), x1)) -> c17(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(0), x1)) -> c17(A__ADD(a__sqr(0), mark(x1)), MARK(x1))
   MARK(add(sqr(nil), x1)) -> c17(A__ADD(a__sqr(nil), mark(x1)), MARK(x1))
   MARK(add(sqr(x0), s(z0))) -> c17(A__ADD(a__sqr(mark(x0)), s(z0)))
   MARK(add(sqr(x0), 0)) -> c17(A__ADD(a__sqr(mark(x0)), 0))
   MARK(add(sqr(x0), nil)) -> c17(A__ADD(a__sqr(mark(x0)), nil))
   MARK(add(sqr(x0), x1)) -> c17(MARK(x1))
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   MARK(add(add(x0, sqr(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(add(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   MARK(add(add(x0, dbl(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(add(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   MARK(add(add(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2))
   MARK(add(add(x0, recip(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(add(x0, s(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), s(z0)), mark(x2)), MARK(x2))
   MARK(add(add(x0, 0), x2)) -> c17(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(x2))
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   MARK(add(add(recip(z0), x1), x2)) -> c17(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(s(z0), x1), x2)) -> c17(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(0, x1), x2)) -> c17(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(nil, x1), x2)) -> c17(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(x0, x1), s(z0))) -> c17(A__ADD(a__add(mark(x0), mark(x1)), s(z0)))
   MARK(add(add(x0, x1), 0)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), 0))
   MARK(add(add(x0, x1), nil)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), nil))
   MARK(add(add(x0, x1), x2)) -> c17(MARK(x2))
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   MARK(add(dbl(sqr(z0)), x1)) -> c17(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(add(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(dbl(dbl(z0)), x1)) -> c17(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(first(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(dbl(cons(z0, z1)), x1)) -> c17(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(recip(z0)), x1)) -> c17(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(s(z0)), x1)) -> c17(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(x1))
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   MARK(add(dbl(nil), x1)) -> c17(A__ADD(a__dbl(nil), mark(x1)), MARK(x1))
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   MARK(add(first(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2))
   MARK(add(first(x0, recip(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, s(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(x2))
   MARK(add(first(x0, 0), x2)) -> c17(A__ADD(a__first(mark(x0), 0), mark(x2)), MARK(x2))
   MARK(add(first(x0, nil), x2)) -> c17(A__ADD(a__first(mark(x0), nil), mark(x2)), MARK(x2))
   MARK(add(first(terms(z0), x1), x2)) -> c17(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(sqr(z0), x1), x2)) -> c17(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(add(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
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   MARK(first(x0, terms(x1))) -> c19(A__FIRST(mark(x0), terms(mark(x1))), MARK(x0))
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   MARK(first(x0, terms(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(first(x0, terms(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, terms(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(first(x0, terms(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, terms(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(first(x0, terms(recip(z0)))) -> c19(A__FIRST(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(first(x0, terms(s(z0)))) -> c19(A__FIRST(mark(x0), a__terms(s(z0))), MARK(x0))
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   MARK(first(x0, terms(nil))) -> c19(A__FIRST(mark(x0), a__terms(nil)), MARK(x0))
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   MARK(first(sqr(z0), terms(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(first(add(z0, z1), terms(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
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   MARK(first(first(z0, z1), terms(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(first(cons(z0, z1), terms(x1))) -> c19(A__FIRST(cons(mark(z0), z1), a__terms(mark(x1))), MARK(cons(z0, z1)))
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S tuples:
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   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
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   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
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   MARK(add(sqr(x0), x1)) -> c17(MARK(x1))
   MARK(add(add(x0, terms(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(add(x0, sqr(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(add(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   MARK(add(add(x0, dbl(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(add(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   MARK(add(add(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2))
   MARK(add(add(x0, recip(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(add(x0, s(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), s(z0)), mark(x2)), MARK(x2))
   MARK(add(add(x0, 0), x2)) -> c17(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(x2))
   MARK(add(add(x0, nil), x2)) -> c17(A__ADD(a__add(mark(x0), nil), mark(x2)), MARK(x2))
   MARK(add(add(terms(z0), x1), x2)) -> c17(A__ADD(a__add(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(sqr(z0), x1), x2)) -> c17(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(add(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(dbl(z0), x1), x2)) -> c17(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(first(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(recip(z0), x1), x2)) -> c17(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(s(z0), x1), x2)) -> c17(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(0, x1), x2)) -> c17(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(nil, x1), x2)) -> c17(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(x0, x1), s(z0))) -> c17(A__ADD(a__add(mark(x0), mark(x1)), s(z0)))
   MARK(add(add(x0, x1), 0)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), 0))
   MARK(add(add(x0, x1), nil)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), nil))
   MARK(add(add(x0, x1), x2)) -> c17(MARK(x2))
   MARK(add(dbl(terms(z0)), x1)) -> c17(A__ADD(a__dbl(a__terms(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(sqr(z0)), x1)) -> c17(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(add(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(dbl(dbl(z0)), x1)) -> c17(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(first(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(dbl(cons(z0, z1)), x1)) -> c17(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(recip(z0)), x1)) -> c17(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(s(z0)), x1)) -> c17(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(x1))
   MARK(add(dbl(0), x1)) -> c17(A__ADD(a__dbl(0), mark(x1)), MARK(x1))
   MARK(add(dbl(nil), x1)) -> c17(A__ADD(a__dbl(nil), mark(x1)), MARK(x1))
   MARK(add(dbl(x0), s(z0))) -> c17(A__ADD(a__dbl(mark(x0)), s(z0)))
   MARK(add(dbl(x0), 0)) -> c17(A__ADD(a__dbl(mark(x0)), 0))
   MARK(add(dbl(x0), nil)) -> c17(A__ADD(a__dbl(mark(x0)), nil))
   MARK(add(dbl(x0), x1)) -> c17(MARK(x1))
   MARK(add(first(x0, terms(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, sqr(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   MARK(add(first(x0, dbl(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   MARK(add(first(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2))
   MARK(add(first(x0, recip(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, s(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(x2))
   MARK(add(first(x0, 0), x2)) -> c17(A__ADD(a__first(mark(x0), 0), mark(x2)), MARK(x2))
   MARK(add(first(x0, nil), x2)) -> c17(A__ADD(a__first(mark(x0), nil), mark(x2)), MARK(x2))
   MARK(add(first(terms(z0), x1), x2)) -> c17(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(sqr(z0), x1), x2)) -> c17(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(add(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(dbl(z0), x1), x2)) -> c17(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(first(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(recip(z0), x1), x2)) -> c17(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(s(z0), x1), x2)) -> c17(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(0, x1), x2)) -> c17(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(nil, x1), x2)) -> c17(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(x0, x1), s(z0))) -> c17(A__ADD(a__first(mark(x0), mark(x1)), s(z0)))
   MARK(add(first(x0, x1), 0)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), 0))
   MARK(add(first(x0, x1), nil)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), nil))
   MARK(add(first(x0, x1), x2)) -> c17(MARK(x2))
   MARK(add(0, s(x1))) -> c17(A__ADD(0, s(x1)))
   MARK(add(0, 0)) -> c17(A__ADD(0, 0))
   MARK(add(0, nil)) -> c17(A__ADD(0, nil))
   MARK(first(x0, terms(x1))) -> c19(A__FIRST(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(first(x0, terms(x1))) -> c19(A__FIRST(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(first(x0, terms(terms(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(first(x0, terms(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(first(x0, terms(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, terms(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(first(x0, terms(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, terms(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(first(x0, terms(recip(z0)))) -> c19(A__FIRST(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(first(x0, terms(s(z0)))) -> c19(A__FIRST(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(first(x0, terms(0))) -> c19(A__FIRST(mark(x0), a__terms(0)), MARK(x0))
   MARK(first(x0, terms(nil))) -> c19(A__FIRST(mark(x0), a__terms(nil)), MARK(x0))
   MARK(first(terms(z0), terms(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(first(sqr(z0), terms(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(first(add(z0, z1), terms(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(first(dbl(z0), terms(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(first(first(z0, z1), terms(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(first(cons(z0, z1), terms(x1))) -> c19(A__FIRST(cons(mark(z0), z1), a__terms(mark(x1))), MARK(cons(z0, z1)))
   MARK(first(recip(z0), terms(x1))) -> c19(A__FIRST(recip(mark(z0)), a__terms(mark(x1))), MARK(recip(z0)))
   MARK(first(s(z0), terms(x1))) -> c19(A__FIRST(s(z0), a__terms(mark(x1))), MARK(s(z0)))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2


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

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

(196)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
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   MARK(add(first(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   MARK(add(first(x0, dbl(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   MARK(add(first(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2))
   MARK(add(first(x0, recip(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, s(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(x2))
   MARK(add(first(x0, 0), x2)) -> c17(A__ADD(a__first(mark(x0), 0), mark(x2)), MARK(x2))
   MARK(add(first(x0, nil), x2)) -> c17(A__ADD(a__first(mark(x0), nil), mark(x2)), MARK(x2))
   MARK(add(first(terms(z0), x1), x2)) -> c17(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(sqr(z0), x1), x2)) -> c17(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(add(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(dbl(z0), x1), x2)) -> c17(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(first(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(recip(z0), x1), x2)) -> c17(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(s(z0), x1), x2)) -> c17(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(0, x1), x2)) -> c17(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(nil, x1), x2)) -> c17(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(x0, x1), s(z0))) -> c17(A__ADD(a__first(mark(x0), mark(x1)), s(z0)))
   MARK(add(first(x0, x1), 0)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), 0))
   MARK(add(first(x0, x1), nil)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), nil))
   MARK(add(first(x0, x1), x2)) -> c17(MARK(x2))
   MARK(add(0, s(x1))) -> c17(A__ADD(0, s(x1)))
   MARK(add(0, 0)) -> c17(A__ADD(0, 0))
   MARK(add(0, nil)) -> c17(A__ADD(0, nil))
   MARK(first(x0, terms(x1))) -> c19(A__FIRST(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(first(x0, terms(terms(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(first(x0, terms(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(first(x0, terms(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, terms(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(first(x0, terms(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, terms(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(first(x0, terms(recip(z0)))) -> c19(A__FIRST(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(first(x0, terms(s(z0)))) -> c19(A__FIRST(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(first(x0, terms(0))) -> c19(A__FIRST(mark(x0), a__terms(0)), MARK(x0))
   MARK(first(x0, terms(nil))) -> c19(A__FIRST(mark(x0), a__terms(nil)), MARK(x0))
   MARK(first(terms(z0), terms(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(first(sqr(z0), terms(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(first(add(z0, z1), terms(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(first(dbl(z0), terms(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(first(first(z0, z1), terms(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(first(x0, terms(x1))) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), terms(x1))) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), terms(x1))) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), terms(x1))) -> c19(A__FIRST(s(z0), a__terms(mark(x1))))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2))))
   MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0))
   MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0))
   MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0))
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   MARK(add(x0, cons(sqr(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(cons(sqr(z0), x2)))
   MARK(add(x0, cons(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(cons(add(z0, z1), x2)))
   MARK(add(x0, cons(dbl(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(cons(dbl(z0), x2)))
   MARK(add(x0, cons(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2)))
   MARK(add(x0, cons(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2)))
   MARK(add(x0, cons(recip(z0), x2))) -> c17(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(cons(recip(z0), x2)))
   MARK(add(x0, cons(s(z0), x2))) -> c17(A__ADD(mark(x0), cons(s(z0), x2)), MARK(cons(s(z0), x2)))
   MARK(add(x0, cons(0, x2))) -> c17(A__ADD(mark(x0), cons(0, x2)), MARK(cons(0, x2)))
   MARK(add(x0, cons(nil, x2))) -> c17(A__ADD(mark(x0), cons(nil, x2)), MARK(cons(nil, x2)))
   MARK(add(terms(z0), cons(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(sqr(z0), cons(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(add(z0, z1), cons(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(dbl(z0), cons(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(first(z0, z1), cons(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(0, cons(x1, x2))) -> c17(A__ADD(0, cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(x0, cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
   MARK(add(cons(z0, z1), cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
   MARK(add(recip(z0), cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
   MARK(add(s(z0), cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
   MARK(add(nil, cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
   MARK(add(x0, recip(terms(z0)))) -> c17(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(recip(terms(z0))))
   MARK(add(x0, recip(sqr(z0)))) -> c17(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(recip(sqr(z0))))
   MARK(add(x0, recip(add(z0, z1)))) -> c17(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(recip(add(z0, z1))))
   MARK(add(x0, recip(dbl(z0)))) -> c17(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(recip(dbl(z0))))
   MARK(add(x0, recip(first(z0, z1)))) -> c17(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(recip(first(z0, z1))))
   MARK(add(x0, recip(cons(z0, z1)))) -> c17(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(recip(cons(z0, z1))))
   MARK(add(x0, recip(recip(z0)))) -> c17(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(recip(recip(z0))))
   MARK(add(x0, recip(s(z0)))) -> c17(A__ADD(mark(x0), recip(s(z0))), MARK(recip(s(z0))))
   MARK(add(x0, recip(0))) -> c17(A__ADD(mark(x0), recip(0)), MARK(recip(0)))
   MARK(add(x0, recip(nil))) -> c17(A__ADD(mark(x0), recip(nil)), MARK(recip(nil)))
   MARK(add(terms(z0), recip(x1))) -> c17(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(sqr(z0), recip(x1))) -> c17(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(add(z0, z1), recip(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(dbl(z0), recip(x1))) -> c17(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(first(z0, z1), recip(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(0, recip(x1))) -> c17(A__ADD(0, recip(mark(x1))), MARK(recip(x1)))
   MARK(add(x0, recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(cons(z0, z1), recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(recip(z0), recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(s(z0), recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(nil, recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(terms(terms(z0)), x1)) -> c17(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(terms(sqr(z0)), x1)) -> c17(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(terms(add(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(terms(dbl(z0)), x1)) -> c17(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(terms(first(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(terms(cons(z0, z1)), x1)) -> c17(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(x1))
   MARK(add(terms(recip(z0)), x1)) -> c17(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(terms(s(z0)), x1)) -> c17(A__ADD(a__terms(s(z0)), mark(x1)), MARK(x1))
   MARK(add(terms(0), x1)) -> c17(A__ADD(a__terms(0), mark(x1)), MARK(x1))
   MARK(add(terms(nil), x1)) -> c17(A__ADD(a__terms(nil), mark(x1)), MARK(x1))
   MARK(add(terms(x0), s(z0))) -> c17(A__ADD(a__terms(mark(x0)), s(z0)))
   MARK(add(terms(x0), 0)) -> c17(A__ADD(a__terms(mark(x0)), 0))
   MARK(add(terms(x0), nil)) -> c17(A__ADD(a__terms(mark(x0)), nil))
   MARK(add(terms(x0), x1)) -> c17(MARK(x1))
   MARK(add(sqr(terms(z0)), x1)) -> c17(A__ADD(a__sqr(a__terms(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(sqr(sqr(z0)), x1)) -> c17(A__ADD(a__sqr(a__sqr(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(sqr(add(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(sqr(dbl(z0)), x1)) -> c17(A__ADD(a__sqr(a__dbl(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(sqr(first(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(sqr(cons(z0, z1)), x1)) -> c17(A__ADD(a__sqr(cons(mark(z0), z1)), mark(x1)), MARK(x1))
   MARK(add(sqr(recip(z0)), x1)) -> c17(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(sqr(s(z0)), x1)) -> c17(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(0), x1)) -> c17(A__ADD(a__sqr(0), mark(x1)), MARK(x1))
   MARK(add(sqr(nil), x1)) -> c17(A__ADD(a__sqr(nil), mark(x1)), MARK(x1))
   MARK(add(sqr(x0), s(z0))) -> c17(A__ADD(a__sqr(mark(x0)), s(z0)))
   MARK(add(sqr(x0), 0)) -> c17(A__ADD(a__sqr(mark(x0)), 0))
   MARK(add(sqr(x0), nil)) -> c17(A__ADD(a__sqr(mark(x0)), nil))
   MARK(add(sqr(x0), x1)) -> c17(MARK(x1))
   MARK(add(add(x0, terms(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(add(x0, sqr(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(add(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   MARK(add(add(x0, dbl(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(add(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   MARK(add(add(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2))
   MARK(add(add(x0, recip(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(add(x0, s(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), s(z0)), mark(x2)), MARK(x2))
   MARK(add(add(x0, 0), x2)) -> c17(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(x2))
   MARK(add(add(x0, nil), x2)) -> c17(A__ADD(a__add(mark(x0), nil), mark(x2)), MARK(x2))
   MARK(add(add(terms(z0), x1), x2)) -> c17(A__ADD(a__add(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(sqr(z0), x1), x2)) -> c17(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(add(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(dbl(z0), x1), x2)) -> c17(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(first(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(recip(z0), x1), x2)) -> c17(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(s(z0), x1), x2)) -> c17(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(0, x1), x2)) -> c17(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(nil, x1), x2)) -> c17(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(x0, x1), s(z0))) -> c17(A__ADD(a__add(mark(x0), mark(x1)), s(z0)))
   MARK(add(add(x0, x1), 0)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), 0))
   MARK(add(add(x0, x1), nil)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), nil))
   MARK(add(add(x0, x1), x2)) -> c17(MARK(x2))
   MARK(add(dbl(terms(z0)), x1)) -> c17(A__ADD(a__dbl(a__terms(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(sqr(z0)), x1)) -> c17(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(add(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(dbl(dbl(z0)), x1)) -> c17(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(first(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(dbl(cons(z0, z1)), x1)) -> c17(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(recip(z0)), x1)) -> c17(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(s(z0)), x1)) -> c17(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(x1))
   MARK(add(dbl(0), x1)) -> c17(A__ADD(a__dbl(0), mark(x1)), MARK(x1))
   MARK(add(dbl(nil), x1)) -> c17(A__ADD(a__dbl(nil), mark(x1)), MARK(x1))
   MARK(add(dbl(x0), s(z0))) -> c17(A__ADD(a__dbl(mark(x0)), s(z0)))
   MARK(add(dbl(x0), 0)) -> c17(A__ADD(a__dbl(mark(x0)), 0))
   MARK(add(dbl(x0), nil)) -> c17(A__ADD(a__dbl(mark(x0)), nil))
   MARK(add(dbl(x0), x1)) -> c17(MARK(x1))
   MARK(add(first(x0, terms(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, sqr(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   MARK(add(first(x0, dbl(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   MARK(add(first(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2))
   MARK(add(first(x0, recip(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, s(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(x2))
   MARK(add(first(x0, 0), x2)) -> c17(A__ADD(a__first(mark(x0), 0), mark(x2)), MARK(x2))
   MARK(add(first(x0, nil), x2)) -> c17(A__ADD(a__first(mark(x0), nil), mark(x2)), MARK(x2))
   MARK(add(first(terms(z0), x1), x2)) -> c17(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(sqr(z0), x1), x2)) -> c17(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(add(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(dbl(z0), x1), x2)) -> c17(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(first(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(recip(z0), x1), x2)) -> c17(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(s(z0), x1), x2)) -> c17(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(0, x1), x2)) -> c17(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(nil, x1), x2)) -> c17(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(x0, x1), s(z0))) -> c17(A__ADD(a__first(mark(x0), mark(x1)), s(z0)))
   MARK(add(first(x0, x1), 0)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), 0))
   MARK(add(first(x0, x1), nil)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), nil))
   MARK(add(first(x0, x1), x2)) -> c17(MARK(x2))
   MARK(add(0, s(x1))) -> c17(A__ADD(0, s(x1)))
   MARK(add(0, 0)) -> c17(A__ADD(0, 0))
   MARK(add(0, nil)) -> c17(A__ADD(0, nil))
   MARK(first(x0, terms(x1))) -> c19(A__FIRST(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(first(x0, terms(terms(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(first(x0, terms(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(first(x0, terms(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, terms(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(first(x0, terms(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, terms(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(first(x0, terms(recip(z0)))) -> c19(A__FIRST(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(first(x0, terms(s(z0)))) -> c19(A__FIRST(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(first(x0, terms(0))) -> c19(A__FIRST(mark(x0), a__terms(0)), MARK(x0))
   MARK(first(x0, terms(nil))) -> c19(A__FIRST(mark(x0), a__terms(nil)), MARK(x0))
   MARK(first(terms(z0), terms(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(first(sqr(z0), terms(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(first(add(z0, z1), terms(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(first(dbl(z0), terms(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(first(first(z0, z1), terms(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(first(x0, terms(x1))) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), terms(x1))) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), terms(x1))) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), terms(x1))) -> c19(A__FIRST(s(z0), a__terms(mark(x1))))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2


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

(197) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) by 
   MARK(first(x0, sqr(x1))) -> c19(A__FIRST(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(first(x0, sqr(terms(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(first(x0, sqr(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(first(x0, sqr(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, sqr(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(first(x0, sqr(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, sqr(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(first(x0, sqr(recip(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(first(x0, sqr(s(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(first(x0, sqr(0))) -> c19(A__FIRST(mark(x0), a__sqr(0)), MARK(x0))
   MARK(first(x0, sqr(nil))) -> c19(A__FIRST(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(first(terms(z0), sqr(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(first(sqr(z0), sqr(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(first(add(z0, z1), sqr(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(first(dbl(z0), sqr(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(first(first(z0, z1), sqr(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(first(cons(z0, z1), sqr(x1))) -> c19(A__FIRST(cons(mark(z0), z1), a__sqr(mark(x1))), MARK(cons(z0, z1)))
   MARK(first(recip(z0), sqr(x1))) -> c19(A__FIRST(recip(mark(z0)), a__sqr(mark(x1))), MARK(recip(z0)))
   MARK(first(s(z0), sqr(x1))) -> c19(A__FIRST(s(z0), a__sqr(mark(x1))), MARK(s(z0)))
   MARK(first(0, sqr(x1))) -> c19(A__FIRST(0, a__sqr(mark(x1))), MARK(0))
   MARK(first(nil, sqr(x1))) -> c19(A__FIRST(nil, a__sqr(mark(x1))), MARK(nil))

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

(198)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2))))
   MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0))
   MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0))
   MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0))
   MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0))
   MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1))))
   MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0))
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   MARK(add(x0, recip(sqr(z0)))) -> c17(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(recip(sqr(z0))))
   MARK(add(x0, recip(add(z0, z1)))) -> c17(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(recip(add(z0, z1))))
   MARK(add(x0, recip(dbl(z0)))) -> c17(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(recip(dbl(z0))))
   MARK(add(x0, recip(first(z0, z1)))) -> c17(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(recip(first(z0, z1))))
   MARK(add(x0, recip(cons(z0, z1)))) -> c17(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(recip(cons(z0, z1))))
   MARK(add(x0, recip(recip(z0)))) -> c17(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(recip(recip(z0))))
   MARK(add(x0, recip(s(z0)))) -> c17(A__ADD(mark(x0), recip(s(z0))), MARK(recip(s(z0))))
   MARK(add(x0, recip(0))) -> c17(A__ADD(mark(x0), recip(0)), MARK(recip(0)))
   MARK(add(x0, recip(nil))) -> c17(A__ADD(mark(x0), recip(nil)), MARK(recip(nil)))
   MARK(add(terms(z0), recip(x1))) -> c17(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(sqr(z0), recip(x1))) -> c17(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(add(z0, z1), recip(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(dbl(z0), recip(x1))) -> c17(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(first(z0, z1), recip(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(0, recip(x1))) -> c17(A__ADD(0, recip(mark(x1))), MARK(recip(x1)))
   MARK(add(x0, recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(cons(z0, z1), recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(recip(z0), recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(s(z0), recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(nil, recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(terms(terms(z0)), x1)) -> c17(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(terms(sqr(z0)), x1)) -> c17(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(terms(add(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(terms(dbl(z0)), x1)) -> c17(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(terms(first(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(terms(cons(z0, z1)), x1)) -> c17(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(x1))
   MARK(add(terms(recip(z0)), x1)) -> c17(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(terms(s(z0)), x1)) -> c17(A__ADD(a__terms(s(z0)), mark(x1)), MARK(x1))
   MARK(add(terms(0), x1)) -> c17(A__ADD(a__terms(0), mark(x1)), MARK(x1))
   MARK(add(terms(nil), x1)) -> c17(A__ADD(a__terms(nil), mark(x1)), MARK(x1))
   MARK(add(terms(x0), s(z0))) -> c17(A__ADD(a__terms(mark(x0)), s(z0)))
   MARK(add(terms(x0), 0)) -> c17(A__ADD(a__terms(mark(x0)), 0))
   MARK(add(terms(x0), nil)) -> c17(A__ADD(a__terms(mark(x0)), nil))
   MARK(add(terms(x0), x1)) -> c17(MARK(x1))
   MARK(add(sqr(terms(z0)), x1)) -> c17(A__ADD(a__sqr(a__terms(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(sqr(sqr(z0)), x1)) -> c17(A__ADD(a__sqr(a__sqr(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(sqr(add(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(sqr(dbl(z0)), x1)) -> c17(A__ADD(a__sqr(a__dbl(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(sqr(first(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(sqr(cons(z0, z1)), x1)) -> c17(A__ADD(a__sqr(cons(mark(z0), z1)), mark(x1)), MARK(x1))
   MARK(add(sqr(recip(z0)), x1)) -> c17(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(sqr(s(z0)), x1)) -> c17(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(0), x1)) -> c17(A__ADD(a__sqr(0), mark(x1)), MARK(x1))
   MARK(add(sqr(nil), x1)) -> c17(A__ADD(a__sqr(nil), mark(x1)), MARK(x1))
   MARK(add(sqr(x0), s(z0))) -> c17(A__ADD(a__sqr(mark(x0)), s(z0)))
   MARK(add(sqr(x0), 0)) -> c17(A__ADD(a__sqr(mark(x0)), 0))
   MARK(add(sqr(x0), nil)) -> c17(A__ADD(a__sqr(mark(x0)), nil))
   MARK(add(sqr(x0), x1)) -> c17(MARK(x1))
   MARK(add(add(x0, terms(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(add(x0, sqr(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(add(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   MARK(add(add(x0, dbl(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(add(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   MARK(add(add(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2))
   MARK(add(add(x0, recip(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(add(x0, s(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), s(z0)), mark(x2)), MARK(x2))
   MARK(add(add(x0, 0), x2)) -> c17(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(x2))
   MARK(add(add(x0, nil), x2)) -> c17(A__ADD(a__add(mark(x0), nil), mark(x2)), MARK(x2))
   MARK(add(add(terms(z0), x1), x2)) -> c17(A__ADD(a__add(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(sqr(z0), x1), x2)) -> c17(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(add(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(dbl(z0), x1), x2)) -> c17(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(first(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(recip(z0), x1), x2)) -> c17(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(s(z0), x1), x2)) -> c17(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(0, x1), x2)) -> c17(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(nil, x1), x2)) -> c17(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(x0, x1), s(z0))) -> c17(A__ADD(a__add(mark(x0), mark(x1)), s(z0)))
   MARK(add(add(x0, x1), 0)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), 0))
   MARK(add(add(x0, x1), nil)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), nil))
   MARK(add(add(x0, x1), x2)) -> c17(MARK(x2))
   MARK(add(dbl(terms(z0)), x1)) -> c17(A__ADD(a__dbl(a__terms(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(sqr(z0)), x1)) -> c17(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(add(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(dbl(dbl(z0)), x1)) -> c17(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(first(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(dbl(cons(z0, z1)), x1)) -> c17(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(recip(z0)), x1)) -> c17(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(s(z0)), x1)) -> c17(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(x1))
   MARK(add(dbl(0), x1)) -> c17(A__ADD(a__dbl(0), mark(x1)), MARK(x1))
   MARK(add(dbl(nil), x1)) -> c17(A__ADD(a__dbl(nil), mark(x1)), MARK(x1))
   MARK(add(dbl(x0), s(z0))) -> c17(A__ADD(a__dbl(mark(x0)), s(z0)))
   MARK(add(dbl(x0), 0)) -> c17(A__ADD(a__dbl(mark(x0)), 0))
   MARK(add(dbl(x0), nil)) -> c17(A__ADD(a__dbl(mark(x0)), nil))
   MARK(add(dbl(x0), x1)) -> c17(MARK(x1))
   MARK(add(first(x0, terms(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, sqr(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   MARK(add(first(x0, dbl(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   MARK(add(first(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2))
   MARK(add(first(x0, recip(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, s(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(x2))
   MARK(add(first(x0, 0), x2)) -> c17(A__ADD(a__first(mark(x0), 0), mark(x2)), MARK(x2))
   MARK(add(first(x0, nil), x2)) -> c17(A__ADD(a__first(mark(x0), nil), mark(x2)), MARK(x2))
   MARK(add(first(terms(z0), x1), x2)) -> c17(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(sqr(z0), x1), x2)) -> c17(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(add(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(dbl(z0), x1), x2)) -> c17(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(first(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(recip(z0), x1), x2)) -> c17(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(s(z0), x1), x2)) -> c17(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(0, x1), x2)) -> c17(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(nil, x1), x2)) -> c17(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(x0, x1), s(z0))) -> c17(A__ADD(a__first(mark(x0), mark(x1)), s(z0)))
   MARK(add(first(x0, x1), 0)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), 0))
   MARK(add(first(x0, x1), nil)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), nil))
   MARK(add(first(x0, x1), x2)) -> c17(MARK(x2))
   MARK(add(0, s(x1))) -> c17(A__ADD(0, s(x1)))
   MARK(add(0, 0)) -> c17(A__ADD(0, 0))
   MARK(add(0, nil)) -> c17(A__ADD(0, nil))
   MARK(first(x0, terms(x1))) -> c19(A__FIRST(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(first(x0, terms(terms(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(first(x0, terms(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(first(x0, terms(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, terms(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(first(x0, terms(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, terms(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(first(x0, terms(recip(z0)))) -> c19(A__FIRST(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(first(x0, terms(s(z0)))) -> c19(A__FIRST(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(first(x0, terms(0))) -> c19(A__FIRST(mark(x0), a__terms(0)), MARK(x0))
   MARK(first(x0, terms(nil))) -> c19(A__FIRST(mark(x0), a__terms(nil)), MARK(x0))
   MARK(first(terms(z0), terms(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(first(sqr(z0), terms(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(first(add(z0, z1), terms(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(first(dbl(z0), terms(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(first(first(z0, z1), terms(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(first(x0, terms(x1))) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), terms(x1))) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), terms(x1))) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), terms(x1))) -> c19(A__FIRST(s(z0), a__terms(mark(x1))))
   MARK(first(x0, sqr(x1))) -> c19(A__FIRST(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(first(x0, sqr(terms(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(first(x0, sqr(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(first(x0, sqr(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, sqr(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(first(x0, sqr(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, sqr(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(first(x0, sqr(recip(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(first(x0, sqr(s(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(first(x0, sqr(0))) -> c19(A__FIRST(mark(x0), a__sqr(0)), MARK(x0))
   MARK(first(x0, sqr(nil))) -> c19(A__FIRST(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(first(terms(z0), sqr(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(first(sqr(z0), sqr(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(first(add(z0, z1), sqr(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(first(dbl(z0), sqr(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(first(first(z0, z1), sqr(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(first(cons(z0, z1), sqr(x1))) -> c19(A__FIRST(cons(mark(z0), z1), a__sqr(mark(x1))), MARK(cons(z0, z1)))
   MARK(first(recip(z0), sqr(x1))) -> c19(A__FIRST(recip(mark(z0)), a__sqr(mark(x1))), MARK(recip(z0)))
   MARK(first(s(z0), sqr(x1))) -> c19(A__FIRST(s(z0), a__sqr(mark(x1))), MARK(s(z0)))
   MARK(first(0, sqr(x1))) -> c19(A__FIRST(0, a__sqr(mark(x1))), MARK(0))
   MARK(first(nil, sqr(x1))) -> c19(A__FIRST(nil, a__sqr(mark(x1))), MARK(nil))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
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   MARK(add(sqr(recip(z0)), x1)) -> c17(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(sqr(s(z0)), x1)) -> c17(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(0), x1)) -> c17(A__ADD(a__sqr(0), mark(x1)), MARK(x1))
   MARK(add(sqr(nil), x1)) -> c17(A__ADD(a__sqr(nil), mark(x1)), MARK(x1))
   MARK(add(sqr(x0), s(z0))) -> c17(A__ADD(a__sqr(mark(x0)), s(z0)))
   MARK(add(sqr(x0), 0)) -> c17(A__ADD(a__sqr(mark(x0)), 0))
   MARK(add(sqr(x0), nil)) -> c17(A__ADD(a__sqr(mark(x0)), nil))
   MARK(add(sqr(x0), x1)) -> c17(MARK(x1))
   MARK(add(add(x0, terms(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(add(x0, sqr(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(add(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   MARK(add(add(x0, dbl(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(add(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   MARK(add(add(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2))
   MARK(add(add(x0, recip(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(add(x0, s(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), s(z0)), mark(x2)), MARK(x2))
   MARK(add(add(x0, 0), x2)) -> c17(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(x2))
   MARK(add(add(x0, nil), x2)) -> c17(A__ADD(a__add(mark(x0), nil), mark(x2)), MARK(x2))
   MARK(add(add(terms(z0), x1), x2)) -> c17(A__ADD(a__add(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(sqr(z0), x1), x2)) -> c17(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(add(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(dbl(z0), x1), x2)) -> c17(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(first(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(recip(z0), x1), x2)) -> c17(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(s(z0), x1), x2)) -> c17(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(0, x1), x2)) -> c17(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(nil, x1), x2)) -> c17(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(x0, x1), s(z0))) -> c17(A__ADD(a__add(mark(x0), mark(x1)), s(z0)))
   MARK(add(add(x0, x1), 0)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), 0))
   MARK(add(add(x0, x1), nil)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), nil))
   MARK(add(add(x0, x1), x2)) -> c17(MARK(x2))
   MARK(add(dbl(terms(z0)), x1)) -> c17(A__ADD(a__dbl(a__terms(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(sqr(z0)), x1)) -> c17(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(add(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(dbl(dbl(z0)), x1)) -> c17(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(first(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(dbl(cons(z0, z1)), x1)) -> c17(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(recip(z0)), x1)) -> c17(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(s(z0)), x1)) -> c17(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(x1))
   MARK(add(dbl(0), x1)) -> c17(A__ADD(a__dbl(0), mark(x1)), MARK(x1))
   MARK(add(dbl(nil), x1)) -> c17(A__ADD(a__dbl(nil), mark(x1)), MARK(x1))
   MARK(add(dbl(x0), s(z0))) -> c17(A__ADD(a__dbl(mark(x0)), s(z0)))
   MARK(add(dbl(x0), 0)) -> c17(A__ADD(a__dbl(mark(x0)), 0))
   MARK(add(dbl(x0), nil)) -> c17(A__ADD(a__dbl(mark(x0)), nil))
   MARK(add(dbl(x0), x1)) -> c17(MARK(x1))
   MARK(add(first(x0, terms(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, sqr(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   MARK(add(first(x0, dbl(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   MARK(add(first(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2))
   MARK(add(first(x0, recip(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, s(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(x2))
   MARK(add(first(x0, 0), x2)) -> c17(A__ADD(a__first(mark(x0), 0), mark(x2)), MARK(x2))
   MARK(add(first(x0, nil), x2)) -> c17(A__ADD(a__first(mark(x0), nil), mark(x2)), MARK(x2))
   MARK(add(first(terms(z0), x1), x2)) -> c17(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(sqr(z0), x1), x2)) -> c17(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(add(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(dbl(z0), x1), x2)) -> c17(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(first(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(recip(z0), x1), x2)) -> c17(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(s(z0), x1), x2)) -> c17(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(0, x1), x2)) -> c17(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(nil, x1), x2)) -> c17(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(x0, x1), s(z0))) -> c17(A__ADD(a__first(mark(x0), mark(x1)), s(z0)))
   MARK(add(first(x0, x1), 0)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), 0))
   MARK(add(first(x0, x1), nil)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), nil))
   MARK(add(first(x0, x1), x2)) -> c17(MARK(x2))
   MARK(add(0, s(x1))) -> c17(A__ADD(0, s(x1)))
   MARK(add(0, 0)) -> c17(A__ADD(0, 0))
   MARK(add(0, nil)) -> c17(A__ADD(0, nil))
   MARK(first(x0, terms(x1))) -> c19(A__FIRST(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(first(x0, terms(terms(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(first(x0, terms(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(first(x0, terms(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, terms(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(first(x0, terms(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, terms(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(first(x0, terms(recip(z0)))) -> c19(A__FIRST(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(first(x0, terms(s(z0)))) -> c19(A__FIRST(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(first(x0, terms(0))) -> c19(A__FIRST(mark(x0), a__terms(0)), MARK(x0))
   MARK(first(x0, terms(nil))) -> c19(A__FIRST(mark(x0), a__terms(nil)), MARK(x0))
   MARK(first(terms(z0), terms(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(first(sqr(z0), terms(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(first(add(z0, z1), terms(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(first(dbl(z0), terms(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(first(first(z0, z1), terms(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(first(x0, terms(x1))) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), terms(x1))) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), terms(x1))) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), terms(x1))) -> c19(A__FIRST(s(z0), a__terms(mark(x1))))
   MARK(first(x0, sqr(x1))) -> c19(A__FIRST(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(first(x0, sqr(terms(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(first(x0, sqr(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(first(x0, sqr(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, sqr(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(first(x0, sqr(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, sqr(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(first(x0, sqr(recip(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(first(x0, sqr(s(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(first(x0, sqr(0))) -> c19(A__FIRST(mark(x0), a__sqr(0)), MARK(x0))
   MARK(first(x0, sqr(nil))) -> c19(A__FIRST(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(first(terms(z0), sqr(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(first(sqr(z0), sqr(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(first(add(z0, z1), sqr(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(first(dbl(z0), sqr(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(first(first(z0, z1), sqr(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(first(cons(z0, z1), sqr(x1))) -> c19(A__FIRST(cons(mark(z0), z1), a__sqr(mark(x1))), MARK(cons(z0, z1)))
   MARK(first(recip(z0), sqr(x1))) -> c19(A__FIRST(recip(mark(z0)), a__sqr(mark(x1))), MARK(recip(z0)))
   MARK(first(s(z0), sqr(x1))) -> c19(A__FIRST(s(z0), a__sqr(mark(x1))), MARK(s(z0)))
   MARK(first(0, sqr(x1))) -> c19(A__FIRST(0, a__sqr(mark(x1))), MARK(0))
   MARK(first(nil, sqr(x1))) -> c19(A__FIRST(nil, a__sqr(mark(x1))), MARK(nil))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2


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

(199) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing nodes:
   MARK(first(nil, sqr(x1))) -> c19(A__FIRST(nil, a__sqr(mark(x1))), MARK(nil))
   MARK(first(0, sqr(x1))) -> c19(A__FIRST(0, a__sqr(mark(x1))), MARK(0))

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

(200)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
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   MARK(add(add(add(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(dbl(z0), x1), x2)) -> c17(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(first(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(recip(z0), x1), x2)) -> c17(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(s(z0), x1), x2)) -> c17(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(0, x1), x2)) -> c17(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(nil, x1), x2)) -> c17(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(x0, x1), s(z0))) -> c17(A__ADD(a__add(mark(x0), mark(x1)), s(z0)))
   MARK(add(add(x0, x1), 0)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), 0))
   MARK(add(add(x0, x1), nil)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), nil))
   MARK(add(add(x0, x1), x2)) -> c17(MARK(x2))
   MARK(add(dbl(terms(z0)), x1)) -> c17(A__ADD(a__dbl(a__terms(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(sqr(z0)), x1)) -> c17(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(add(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(dbl(dbl(z0)), x1)) -> c17(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(first(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(dbl(cons(z0, z1)), x1)) -> c17(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(recip(z0)), x1)) -> c17(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(s(z0)), x1)) -> c17(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(x1))
   MARK(add(dbl(0), x1)) -> c17(A__ADD(a__dbl(0), mark(x1)), MARK(x1))
   MARK(add(dbl(nil), x1)) -> c17(A__ADD(a__dbl(nil), mark(x1)), MARK(x1))
   MARK(add(dbl(x0), s(z0))) -> c17(A__ADD(a__dbl(mark(x0)), s(z0)))
   MARK(add(dbl(x0), 0)) -> c17(A__ADD(a__dbl(mark(x0)), 0))
   MARK(add(dbl(x0), nil)) -> c17(A__ADD(a__dbl(mark(x0)), nil))
   MARK(add(dbl(x0), x1)) -> c17(MARK(x1))
   MARK(add(first(x0, terms(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, sqr(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   MARK(add(first(x0, dbl(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   MARK(add(first(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2))
   MARK(add(first(x0, recip(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, s(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(x2))
   MARK(add(first(x0, 0), x2)) -> c17(A__ADD(a__first(mark(x0), 0), mark(x2)), MARK(x2))
   MARK(add(first(x0, nil), x2)) -> c17(A__ADD(a__first(mark(x0), nil), mark(x2)), MARK(x2))
   MARK(add(first(terms(z0), x1), x2)) -> c17(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(sqr(z0), x1), x2)) -> c17(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(add(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(dbl(z0), x1), x2)) -> c17(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(first(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(recip(z0), x1), x2)) -> c17(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(s(z0), x1), x2)) -> c17(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(0, x1), x2)) -> c17(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(nil, x1), x2)) -> c17(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(x0, x1), s(z0))) -> c17(A__ADD(a__first(mark(x0), mark(x1)), s(z0)))
   MARK(add(first(x0, x1), 0)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), 0))
   MARK(add(first(x0, x1), nil)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), nil))
   MARK(add(first(x0, x1), x2)) -> c17(MARK(x2))
   MARK(add(0, s(x1))) -> c17(A__ADD(0, s(x1)))
   MARK(add(0, 0)) -> c17(A__ADD(0, 0))
   MARK(add(0, nil)) -> c17(A__ADD(0, nil))
   MARK(first(x0, terms(x1))) -> c19(A__FIRST(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(first(x0, terms(terms(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(first(x0, terms(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(first(x0, terms(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, terms(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(first(x0, terms(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, terms(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(first(x0, terms(recip(z0)))) -> c19(A__FIRST(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(first(x0, terms(s(z0)))) -> c19(A__FIRST(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(first(x0, terms(0))) -> c19(A__FIRST(mark(x0), a__terms(0)), MARK(x0))
   MARK(first(x0, terms(nil))) -> c19(A__FIRST(mark(x0), a__terms(nil)), MARK(x0))
   MARK(first(terms(z0), terms(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(first(sqr(z0), terms(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(first(add(z0, z1), terms(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(first(dbl(z0), terms(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(first(first(z0, z1), terms(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(first(x0, terms(x1))) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), terms(x1))) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), terms(x1))) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), terms(x1))) -> c19(A__FIRST(s(z0), a__terms(mark(x1))))
   MARK(first(x0, sqr(x1))) -> c19(A__FIRST(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(first(x0, sqr(terms(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(first(x0, sqr(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(first(x0, sqr(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, sqr(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(first(x0, sqr(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, sqr(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(first(x0, sqr(recip(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(first(x0, sqr(s(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(first(x0, sqr(0))) -> c19(A__FIRST(mark(x0), a__sqr(0)), MARK(x0))
   MARK(first(x0, sqr(nil))) -> c19(A__FIRST(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(first(terms(z0), sqr(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(first(sqr(z0), sqr(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(first(add(z0, z1), sqr(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(first(dbl(z0), sqr(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(first(first(z0, z1), sqr(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(first(cons(z0, z1), sqr(x1))) -> c19(A__FIRST(cons(mark(z0), z1), a__sqr(mark(x1))), MARK(cons(z0, z1)))
   MARK(first(recip(z0), sqr(x1))) -> c19(A__FIRST(recip(mark(z0)), a__sqr(mark(x1))), MARK(recip(z0)))
   MARK(first(s(z0), sqr(x1))) -> c19(A__FIRST(s(z0), a__sqr(mark(x1))), MARK(s(z0)))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
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   MARK(add(first(sqr(z0), x1), x2)) -> c17(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(add(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(dbl(z0), x1), x2)) -> c17(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(first(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(recip(z0), x1), x2)) -> c17(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(s(z0), x1), x2)) -> c17(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(0, x1), x2)) -> c17(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(nil, x1), x2)) -> c17(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(x0, x1), s(z0))) -> c17(A__ADD(a__first(mark(x0), mark(x1)), s(z0)))
   MARK(add(first(x0, x1), 0)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), 0))
   MARK(add(first(x0, x1), nil)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), nil))
   MARK(add(first(x0, x1), x2)) -> c17(MARK(x2))
   MARK(add(0, s(x1))) -> c17(A__ADD(0, s(x1)))
   MARK(add(0, 0)) -> c17(A__ADD(0, 0))
   MARK(add(0, nil)) -> c17(A__ADD(0, nil))
   MARK(first(x0, terms(x1))) -> c19(A__FIRST(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(first(x0, terms(terms(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(first(x0, terms(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(first(x0, terms(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, terms(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(first(x0, terms(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, terms(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(first(x0, terms(recip(z0)))) -> c19(A__FIRST(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(first(x0, terms(s(z0)))) -> c19(A__FIRST(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(first(x0, terms(0))) -> c19(A__FIRST(mark(x0), a__terms(0)), MARK(x0))
   MARK(first(x0, terms(nil))) -> c19(A__FIRST(mark(x0), a__terms(nil)), MARK(x0))
   MARK(first(terms(z0), terms(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(first(sqr(z0), terms(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(first(add(z0, z1), terms(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(first(dbl(z0), terms(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(first(first(z0, z1), terms(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(first(x0, terms(x1))) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), terms(x1))) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), terms(x1))) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), terms(x1))) -> c19(A__FIRST(s(z0), a__terms(mark(x1))))
   MARK(first(x0, sqr(x1))) -> c19(A__FIRST(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(first(x0, sqr(terms(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(first(x0, sqr(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(first(x0, sqr(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, sqr(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(first(x0, sqr(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, sqr(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(first(x0, sqr(recip(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(first(x0, sqr(s(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(first(x0, sqr(0))) -> c19(A__FIRST(mark(x0), a__sqr(0)), MARK(x0))
   MARK(first(x0, sqr(nil))) -> c19(A__FIRST(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(first(terms(z0), sqr(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(first(sqr(z0), sqr(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(first(add(z0, z1), sqr(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(first(dbl(z0), sqr(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(first(first(z0, z1), sqr(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(first(cons(z0, z1), sqr(x1))) -> c19(A__FIRST(cons(mark(z0), z1), a__sqr(mark(x1))), MARK(cons(z0, z1)))
   MARK(first(recip(z0), sqr(x1))) -> c19(A__FIRST(recip(mark(z0)), a__sqr(mark(x1))), MARK(recip(z0)))
   MARK(first(s(z0), sqr(x1))) -> c19(A__FIRST(s(z0), a__sqr(mark(x1))), MARK(s(z0)))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2


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

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

(202)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
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   MARK(first(x0, terms(recip(z0)))) -> c19(A__FIRST(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(first(x0, terms(s(z0)))) -> c19(A__FIRST(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(first(x0, terms(0))) -> c19(A__FIRST(mark(x0), a__terms(0)), MARK(x0))
   MARK(first(x0, terms(nil))) -> c19(A__FIRST(mark(x0), a__terms(nil)), MARK(x0))
   MARK(first(terms(z0), terms(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(first(sqr(z0), terms(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(first(add(z0, z1), terms(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(first(dbl(z0), terms(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(first(first(z0, z1), terms(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(first(x0, terms(x1))) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), terms(x1))) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), terms(x1))) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), terms(x1))) -> c19(A__FIRST(s(z0), a__terms(mark(x1))))
   MARK(first(x0, sqr(terms(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(first(x0, sqr(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(first(x0, sqr(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, sqr(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(first(x0, sqr(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, sqr(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(first(x0, sqr(recip(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(first(x0, sqr(s(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(first(x0, sqr(0))) -> c19(A__FIRST(mark(x0), a__sqr(0)), MARK(x0))
   MARK(first(x0, sqr(nil))) -> c19(A__FIRST(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(first(terms(z0), sqr(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(first(sqr(z0), sqr(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(first(add(z0, z1), sqr(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(first(dbl(z0), sqr(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(first(first(z0, z1), sqr(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(first(x0, sqr(x1))) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), sqr(x1))) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), sqr(x1))) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), sqr(x1))) -> c19(A__FIRST(s(z0), a__sqr(mark(x1))))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2))))
   MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0))
   MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0))
   MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0))
   MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0))
   MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1))))
   MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
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   MARK(add(dbl(z0), cons(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(first(z0, z1), cons(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(0, cons(x1, x2))) -> c17(A__ADD(0, cons(mark(x1), x2)), MARK(cons(x1, x2)))
   MARK(add(x0, cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
   MARK(add(cons(z0, z1), cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
   MARK(add(recip(z0), cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
   MARK(add(s(z0), cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
   MARK(add(nil, cons(x1, x2))) -> c17(MARK(cons(x1, x2)))
   MARK(add(x0, recip(terms(z0)))) -> c17(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(recip(terms(z0))))
   MARK(add(x0, recip(sqr(z0)))) -> c17(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(recip(sqr(z0))))
   MARK(add(x0, recip(add(z0, z1)))) -> c17(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(recip(add(z0, z1))))
   MARK(add(x0, recip(dbl(z0)))) -> c17(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(recip(dbl(z0))))
   MARK(add(x0, recip(first(z0, z1)))) -> c17(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(recip(first(z0, z1))))
   MARK(add(x0, recip(cons(z0, z1)))) -> c17(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(recip(cons(z0, z1))))
   MARK(add(x0, recip(recip(z0)))) -> c17(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(recip(recip(z0))))
   MARK(add(x0, recip(s(z0)))) -> c17(A__ADD(mark(x0), recip(s(z0))), MARK(recip(s(z0))))
   MARK(add(x0, recip(0))) -> c17(A__ADD(mark(x0), recip(0)), MARK(recip(0)))
   MARK(add(x0, recip(nil))) -> c17(A__ADD(mark(x0), recip(nil)), MARK(recip(nil)))
   MARK(add(terms(z0), recip(x1))) -> c17(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(sqr(z0), recip(x1))) -> c17(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(add(z0, z1), recip(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(dbl(z0), recip(x1))) -> c17(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(first(z0, z1), recip(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1)))
   MARK(add(0, recip(x1))) -> c17(A__ADD(0, recip(mark(x1))), MARK(recip(x1)))
   MARK(add(x0, recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(cons(z0, z1), recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(recip(z0), recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(s(z0), recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(nil, recip(x1))) -> c17(MARK(recip(x1)))
   MARK(add(terms(terms(z0)), x1)) -> c17(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(terms(sqr(z0)), x1)) -> c17(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(terms(add(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(terms(dbl(z0)), x1)) -> c17(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(terms(first(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(terms(cons(z0, z1)), x1)) -> c17(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(x1))
   MARK(add(terms(recip(z0)), x1)) -> c17(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(terms(s(z0)), x1)) -> c17(A__ADD(a__terms(s(z0)), mark(x1)), MARK(x1))
   MARK(add(terms(0), x1)) -> c17(A__ADD(a__terms(0), mark(x1)), MARK(x1))
   MARK(add(terms(nil), x1)) -> c17(A__ADD(a__terms(nil), mark(x1)), MARK(x1))
   MARK(add(terms(x0), s(z0))) -> c17(A__ADD(a__terms(mark(x0)), s(z0)))
   MARK(add(terms(x0), 0)) -> c17(A__ADD(a__terms(mark(x0)), 0))
   MARK(add(terms(x0), nil)) -> c17(A__ADD(a__terms(mark(x0)), nil))
   MARK(add(terms(x0), x1)) -> c17(MARK(x1))
   MARK(add(sqr(terms(z0)), x1)) -> c17(A__ADD(a__sqr(a__terms(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(sqr(sqr(z0)), x1)) -> c17(A__ADD(a__sqr(a__sqr(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(sqr(add(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(sqr(dbl(z0)), x1)) -> c17(A__ADD(a__sqr(a__dbl(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(sqr(first(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(sqr(cons(z0, z1)), x1)) -> c17(A__ADD(a__sqr(cons(mark(z0), z1)), mark(x1)), MARK(x1))
   MARK(add(sqr(recip(z0)), x1)) -> c17(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(sqr(s(z0)), x1)) -> c17(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(x1))
   MARK(add(sqr(0), x1)) -> c17(A__ADD(a__sqr(0), mark(x1)), MARK(x1))
   MARK(add(sqr(nil), x1)) -> c17(A__ADD(a__sqr(nil), mark(x1)), MARK(x1))
   MARK(add(sqr(x0), s(z0))) -> c17(A__ADD(a__sqr(mark(x0)), s(z0)))
   MARK(add(sqr(x0), 0)) -> c17(A__ADD(a__sqr(mark(x0)), 0))
   MARK(add(sqr(x0), nil)) -> c17(A__ADD(a__sqr(mark(x0)), nil))
   MARK(add(sqr(x0), x1)) -> c17(MARK(x1))
   MARK(add(add(x0, terms(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(add(x0, sqr(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(add(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   MARK(add(add(x0, dbl(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(add(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   MARK(add(add(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2))
   MARK(add(add(x0, recip(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(add(x0, s(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), s(z0)), mark(x2)), MARK(x2))
   MARK(add(add(x0, 0), x2)) -> c17(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(x2))
   MARK(add(add(x0, nil), x2)) -> c17(A__ADD(a__add(mark(x0), nil), mark(x2)), MARK(x2))
   MARK(add(add(terms(z0), x1), x2)) -> c17(A__ADD(a__add(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(sqr(z0), x1), x2)) -> c17(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(add(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(dbl(z0), x1), x2)) -> c17(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(first(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(recip(z0), x1), x2)) -> c17(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(s(z0), x1), x2)) -> c17(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(0, x1), x2)) -> c17(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(nil, x1), x2)) -> c17(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(x0, x1), s(z0))) -> c17(A__ADD(a__add(mark(x0), mark(x1)), s(z0)))
   MARK(add(add(x0, x1), 0)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), 0))
   MARK(add(add(x0, x1), nil)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), nil))
   MARK(add(add(x0, x1), x2)) -> c17(MARK(x2))
   MARK(add(dbl(terms(z0)), x1)) -> c17(A__ADD(a__dbl(a__terms(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(sqr(z0)), x1)) -> c17(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(add(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(dbl(dbl(z0)), x1)) -> c17(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(first(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(dbl(cons(z0, z1)), x1)) -> c17(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(recip(z0)), x1)) -> c17(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(s(z0)), x1)) -> c17(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(x1))
   MARK(add(dbl(0), x1)) -> c17(A__ADD(a__dbl(0), mark(x1)), MARK(x1))
   MARK(add(dbl(nil), x1)) -> c17(A__ADD(a__dbl(nil), mark(x1)), MARK(x1))
   MARK(add(dbl(x0), s(z0))) -> c17(A__ADD(a__dbl(mark(x0)), s(z0)))
   MARK(add(dbl(x0), 0)) -> c17(A__ADD(a__dbl(mark(x0)), 0))
   MARK(add(dbl(x0), nil)) -> c17(A__ADD(a__dbl(mark(x0)), nil))
   MARK(add(dbl(x0), x1)) -> c17(MARK(x1))
   MARK(add(first(x0, terms(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, sqr(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   MARK(add(first(x0, dbl(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   MARK(add(first(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2))
   MARK(add(first(x0, recip(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, s(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(x2))
   MARK(add(first(x0, 0), x2)) -> c17(A__ADD(a__first(mark(x0), 0), mark(x2)), MARK(x2))
   MARK(add(first(x0, nil), x2)) -> c17(A__ADD(a__first(mark(x0), nil), mark(x2)), MARK(x2))
   MARK(add(first(terms(z0), x1), x2)) -> c17(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(sqr(z0), x1), x2)) -> c17(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(add(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(dbl(z0), x1), x2)) -> c17(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(first(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(recip(z0), x1), x2)) -> c17(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(s(z0), x1), x2)) -> c17(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(0, x1), x2)) -> c17(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(nil, x1), x2)) -> c17(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(x0, x1), s(z0))) -> c17(A__ADD(a__first(mark(x0), mark(x1)), s(z0)))
   MARK(add(first(x0, x1), 0)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), 0))
   MARK(add(first(x0, x1), nil)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), nil))
   MARK(add(first(x0, x1), x2)) -> c17(MARK(x2))
   MARK(add(0, s(x1))) -> c17(A__ADD(0, s(x1)))
   MARK(add(0, 0)) -> c17(A__ADD(0, 0))
   MARK(add(0, nil)) -> c17(A__ADD(0, nil))
   MARK(first(x0, terms(x1))) -> c19(A__FIRST(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(first(x0, terms(terms(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(first(x0, terms(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(first(x0, terms(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, terms(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(first(x0, terms(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, terms(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(first(x0, terms(recip(z0)))) -> c19(A__FIRST(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(first(x0, terms(s(z0)))) -> c19(A__FIRST(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(first(x0, terms(0))) -> c19(A__FIRST(mark(x0), a__terms(0)), MARK(x0))
   MARK(first(x0, terms(nil))) -> c19(A__FIRST(mark(x0), a__terms(nil)), MARK(x0))
   MARK(first(terms(z0), terms(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(first(sqr(z0), terms(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(first(add(z0, z1), terms(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(first(dbl(z0), terms(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(first(first(z0, z1), terms(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(first(x0, terms(x1))) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), terms(x1))) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), terms(x1))) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), terms(x1))) -> c19(A__FIRST(s(z0), a__terms(mark(x1))))
   MARK(first(x0, sqr(terms(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(first(x0, sqr(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(first(x0, sqr(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, sqr(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(first(x0, sqr(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, sqr(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(first(x0, sqr(recip(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(first(x0, sqr(s(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(first(x0, sqr(0))) -> c19(A__FIRST(mark(x0), a__sqr(0)), MARK(x0))
   MARK(first(x0, sqr(nil))) -> c19(A__FIRST(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(first(terms(z0), sqr(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(first(sqr(z0), sqr(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(first(add(z0, z1), sqr(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(first(dbl(z0), sqr(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(first(first(z0, z1), sqr(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(first(x0, sqr(x1))) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), sqr(x1))) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), sqr(x1))) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), sqr(x1))) -> c19(A__FIRST(s(z0), a__sqr(mark(x1))))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2


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

(203) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) by 
   MARK(first(x0, add(x1, x2))) -> c19(A__FIRST(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(first(x0, add(x1, terms(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(first(x0, add(x1, sqr(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(first(x0, add(x1, add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, add(x1, dbl(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(first(x0, add(x1, first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, add(x1, cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(first(x0, add(x1, recip(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(first(x0, add(x1, s(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(first(x0, add(x1, 0))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(first(x0, add(x1, nil))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(first(x0, add(terms(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, add(sqr(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, add(add(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(first(x0, add(dbl(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, add(first(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(first(x0, add(cons(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(first(x0, add(recip(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, add(s(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(first(x0, add(0, x2))) -> c19(A__FIRST(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(first(x0, add(nil, x2))) -> c19(A__FIRST(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(first(terms(z0), add(x1, x2))) -> c19(A__FIRST(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(first(sqr(z0), add(x1, x2))) -> c19(A__FIRST(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(first(add(z0, z1), add(x1, x2))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(first(dbl(z0), add(x1, x2))) -> c19(A__FIRST(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(first(first(z0, z1), add(x1, x2))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(first(cons(z0, z1), add(x1, x2))) -> c19(A__FIRST(cons(mark(z0), z1), a__add(mark(x1), mark(x2))), MARK(cons(z0, z1)))
   MARK(first(recip(z0), add(x1, x2))) -> c19(A__FIRST(recip(mark(z0)), a__add(mark(x1), mark(x2))), MARK(recip(z0)))
   MARK(first(s(z0), add(x1, x2))) -> c19(A__FIRST(s(z0), a__add(mark(x1), mark(x2))), MARK(s(z0)))
   MARK(first(0, add(x1, x2))) -> c19(A__FIRST(0, a__add(mark(x1), mark(x2))), MARK(0))
   MARK(first(nil, add(x1, x2))) -> c19(A__FIRST(nil, a__add(mark(x1), mark(x2))), MARK(nil))

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

(204)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2))))
   MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0))
   MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0))
   MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0))
   MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0))
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   MARK(first(add(z0, z1), sqr(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(first(dbl(z0), sqr(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(first(first(z0, z1), sqr(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(first(x0, sqr(x1))) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), sqr(x1))) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), sqr(x1))) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), sqr(x1))) -> c19(A__FIRST(s(z0), a__sqr(mark(x1))))
   MARK(first(x0, add(x1, x2))) -> c19(A__FIRST(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(first(x0, add(x1, terms(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(first(x0, add(x1, sqr(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(first(x0, add(x1, add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, add(x1, dbl(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(first(x0, add(x1, first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, add(x1, cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(first(x0, add(x1, recip(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(first(x0, add(x1, s(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(first(x0, add(x1, 0))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(first(x0, add(x1, nil))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(first(x0, add(terms(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, add(sqr(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, add(add(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(first(x0, add(dbl(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, add(first(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(first(x0, add(cons(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(first(x0, add(recip(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, add(s(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(first(x0, add(0, x2))) -> c19(A__FIRST(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(first(x0, add(nil, x2))) -> c19(A__FIRST(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(first(terms(z0), add(x1, x2))) -> c19(A__FIRST(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(first(sqr(z0), add(x1, x2))) -> c19(A__FIRST(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(first(add(z0, z1), add(x1, x2))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(first(dbl(z0), add(x1, x2))) -> c19(A__FIRST(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(first(first(z0, z1), add(x1, x2))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(first(cons(z0, z1), add(x1, x2))) -> c19(A__FIRST(cons(mark(z0), z1), a__add(mark(x1), mark(x2))), MARK(cons(z0, z1)))
   MARK(first(recip(z0), add(x1, x2))) -> c19(A__FIRST(recip(mark(z0)), a__add(mark(x1), mark(x2))), MARK(recip(z0)))
   MARK(first(s(z0), add(x1, x2))) -> c19(A__FIRST(s(z0), a__add(mark(x1), mark(x2))), MARK(s(z0)))
   MARK(first(0, add(x1, x2))) -> c19(A__FIRST(0, a__add(mark(x1), mark(x2))), MARK(0))
   MARK(first(nil, add(x1, x2))) -> c19(A__FIRST(nil, a__add(mark(x1), mark(x2))), MARK(nil))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2))))
   MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0))
   MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0))
   MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0))
   MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0))
   MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0)))
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   MARK(first(cons(z0, z1), sqr(x1))) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), sqr(x1))) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), sqr(x1))) -> c19(A__FIRST(s(z0), a__sqr(mark(x1))))
   MARK(first(x0, add(x1, x2))) -> c19(A__FIRST(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(first(x0, add(x1, terms(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(first(x0, add(x1, sqr(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(first(x0, add(x1, add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, add(x1, dbl(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(first(x0, add(x1, first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, add(x1, cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(first(x0, add(x1, recip(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(first(x0, add(x1, s(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(first(x0, add(x1, 0))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(first(x0, add(x1, nil))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(first(x0, add(terms(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, add(sqr(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, add(add(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(first(x0, add(dbl(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, add(first(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(first(x0, add(cons(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(first(x0, add(recip(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, add(s(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(first(x0, add(0, x2))) -> c19(A__FIRST(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(first(x0, add(nil, x2))) -> c19(A__FIRST(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(first(terms(z0), add(x1, x2))) -> c19(A__FIRST(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(first(sqr(z0), add(x1, x2))) -> c19(A__FIRST(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(first(add(z0, z1), add(x1, x2))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(first(dbl(z0), add(x1, x2))) -> c19(A__FIRST(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(first(first(z0, z1), add(x1, x2))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(first(cons(z0, z1), add(x1, x2))) -> c19(A__FIRST(cons(mark(z0), z1), a__add(mark(x1), mark(x2))), MARK(cons(z0, z1)))
   MARK(first(recip(z0), add(x1, x2))) -> c19(A__FIRST(recip(mark(z0)), a__add(mark(x1), mark(x2))), MARK(recip(z0)))
   MARK(first(s(z0), add(x1, x2))) -> c19(A__FIRST(s(z0), a__add(mark(x1), mark(x2))), MARK(s(z0)))
   MARK(first(0, add(x1, x2))) -> c19(A__FIRST(0, a__add(mark(x1), mark(x2))), MARK(0))
   MARK(first(nil, add(x1, x2))) -> c19(A__FIRST(nil, a__add(mark(x1), mark(x2))), MARK(nil))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2


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

(205) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing nodes:
   MARK(first(0, add(x1, x2))) -> c19(A__FIRST(0, a__add(mark(x1), mark(x2))), MARK(0))
   MARK(first(nil, add(x1, x2))) -> c19(A__FIRST(nil, a__add(mark(x1), mark(x2))), MARK(nil))

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

(206)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2))))
   MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0))
   MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0))
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   MARK(first(x0, sqr(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, sqr(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(first(x0, sqr(recip(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(first(x0, sqr(s(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(first(x0, sqr(0))) -> c19(A__FIRST(mark(x0), a__sqr(0)), MARK(x0))
   MARK(first(x0, sqr(nil))) -> c19(A__FIRST(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(first(terms(z0), sqr(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(first(sqr(z0), sqr(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(first(add(z0, z1), sqr(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(first(dbl(z0), sqr(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(first(first(z0, z1), sqr(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(first(x0, sqr(x1))) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), sqr(x1))) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), sqr(x1))) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), sqr(x1))) -> c19(A__FIRST(s(z0), a__sqr(mark(x1))))
   MARK(first(x0, add(x1, x2))) -> c19(A__FIRST(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(first(x0, add(x1, terms(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(first(x0, add(x1, sqr(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(first(x0, add(x1, add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, add(x1, dbl(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(first(x0, add(x1, first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, add(x1, cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(first(x0, add(x1, recip(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(first(x0, add(x1, s(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(first(x0, add(x1, 0))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(first(x0, add(x1, nil))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(first(x0, add(terms(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, add(sqr(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, add(add(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(first(x0, add(dbl(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, add(first(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(first(x0, add(cons(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(first(x0, add(recip(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, add(s(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(first(x0, add(0, x2))) -> c19(A__FIRST(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(first(x0, add(nil, x2))) -> c19(A__FIRST(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(first(terms(z0), add(x1, x2))) -> c19(A__FIRST(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(first(sqr(z0), add(x1, x2))) -> c19(A__FIRST(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(first(add(z0, z1), add(x1, x2))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(first(dbl(z0), add(x1, x2))) -> c19(A__FIRST(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(first(first(z0, z1), add(x1, x2))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(first(cons(z0, z1), add(x1, x2))) -> c19(A__FIRST(cons(mark(z0), z1), a__add(mark(x1), mark(x2))), MARK(cons(z0, z1)))
   MARK(first(recip(z0), add(x1, x2))) -> c19(A__FIRST(recip(mark(z0)), a__add(mark(x1), mark(x2))), MARK(recip(z0)))
   MARK(first(s(z0), add(x1, x2))) -> c19(A__FIRST(s(z0), a__add(mark(x1), mark(x2))), MARK(s(z0)))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2))))
   MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0))
   MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0))
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   MARK(first(terms(z0), sqr(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(first(sqr(z0), sqr(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(first(add(z0, z1), sqr(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(first(dbl(z0), sqr(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(first(first(z0, z1), sqr(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(first(x0, sqr(x1))) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), sqr(x1))) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), sqr(x1))) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), sqr(x1))) -> c19(A__FIRST(s(z0), a__sqr(mark(x1))))
   MARK(first(x0, add(x1, x2))) -> c19(A__FIRST(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(first(x0, add(x1, terms(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(first(x0, add(x1, sqr(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(first(x0, add(x1, add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, add(x1, dbl(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(first(x0, add(x1, first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, add(x1, cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(first(x0, add(x1, recip(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(first(x0, add(x1, s(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(first(x0, add(x1, 0))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(first(x0, add(x1, nil))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(first(x0, add(terms(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, add(sqr(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, add(add(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(first(x0, add(dbl(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, add(first(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(first(x0, add(cons(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(first(x0, add(recip(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, add(s(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(first(x0, add(0, x2))) -> c19(A__FIRST(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(first(x0, add(nil, x2))) -> c19(A__FIRST(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(first(terms(z0), add(x1, x2))) -> c19(A__FIRST(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(first(sqr(z0), add(x1, x2))) -> c19(A__FIRST(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(first(add(z0, z1), add(x1, x2))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(first(dbl(z0), add(x1, x2))) -> c19(A__FIRST(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(first(first(z0, z1), add(x1, x2))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(first(cons(z0, z1), add(x1, x2))) -> c19(A__FIRST(cons(mark(z0), z1), a__add(mark(x1), mark(x2))), MARK(cons(z0, z1)))
   MARK(first(recip(z0), add(x1, x2))) -> c19(A__FIRST(recip(mark(z0)), a__add(mark(x1), mark(x2))), MARK(recip(z0)))
   MARK(first(s(z0), add(x1, x2))) -> c19(A__FIRST(s(z0), a__add(mark(x1), mark(x2))), MARK(s(z0)))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2


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

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

(208)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2))))
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   MARK(first(x0, sqr(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, sqr(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(first(x0, sqr(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, sqr(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(first(x0, sqr(recip(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(first(x0, sqr(s(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(first(x0, sqr(0))) -> c19(A__FIRST(mark(x0), a__sqr(0)), MARK(x0))
   MARK(first(x0, sqr(nil))) -> c19(A__FIRST(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(first(terms(z0), sqr(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(first(sqr(z0), sqr(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(first(add(z0, z1), sqr(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(first(dbl(z0), sqr(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(first(first(z0, z1), sqr(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(first(x0, sqr(x1))) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), sqr(x1))) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), sqr(x1))) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), sqr(x1))) -> c19(A__FIRST(s(z0), a__sqr(mark(x1))))
   MARK(first(x0, add(x1, terms(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(first(x0, add(x1, sqr(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(first(x0, add(x1, add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, add(x1, dbl(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(first(x0, add(x1, first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, add(x1, cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(first(x0, add(x1, recip(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(first(x0, add(x1, s(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(first(x0, add(x1, 0))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(first(x0, add(x1, nil))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(first(x0, add(terms(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, add(sqr(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, add(add(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(first(x0, add(dbl(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, add(first(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(first(x0, add(cons(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(first(x0, add(recip(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, add(s(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(first(x0, add(0, x2))) -> c19(A__FIRST(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(first(x0, add(nil, x2))) -> c19(A__FIRST(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(first(terms(z0), add(x1, x2))) -> c19(A__FIRST(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(first(sqr(z0), add(x1, x2))) -> c19(A__FIRST(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(first(add(z0, z1), add(x1, x2))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(first(dbl(z0), add(x1, x2))) -> c19(A__FIRST(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(first(first(z0, z1), add(x1, x2))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(first(x0, add(x1, x2))) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), add(x1, x2))) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), add(x1, x2))) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), add(x1, x2))) -> c19(A__FIRST(s(z0), a__add(mark(x1), mark(x2))))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2))))
   MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0))
   MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0))
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   MARK(first(x0, sqr(0))) -> c19(A__FIRST(mark(x0), a__sqr(0)), MARK(x0))
   MARK(first(x0, sqr(nil))) -> c19(A__FIRST(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(first(terms(z0), sqr(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(first(sqr(z0), sqr(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(first(add(z0, z1), sqr(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(first(dbl(z0), sqr(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(first(first(z0, z1), sqr(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(first(x0, sqr(x1))) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), sqr(x1))) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), sqr(x1))) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), sqr(x1))) -> c19(A__FIRST(s(z0), a__sqr(mark(x1))))
   MARK(first(x0, add(x1, terms(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(first(x0, add(x1, sqr(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(first(x0, add(x1, add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, add(x1, dbl(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(first(x0, add(x1, first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, add(x1, cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(first(x0, add(x1, recip(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(first(x0, add(x1, s(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(first(x0, add(x1, 0))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(first(x0, add(x1, nil))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(first(x0, add(terms(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, add(sqr(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, add(add(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(first(x0, add(dbl(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, add(first(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(first(x0, add(cons(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(first(x0, add(recip(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, add(s(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(first(x0, add(0, x2))) -> c19(A__FIRST(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(first(x0, add(nil, x2))) -> c19(A__FIRST(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(first(terms(z0), add(x1, x2))) -> c19(A__FIRST(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(first(sqr(z0), add(x1, x2))) -> c19(A__FIRST(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(first(add(z0, z1), add(x1, x2))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(first(dbl(z0), add(x1, x2))) -> c19(A__FIRST(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(first(first(z0, z1), add(x1, x2))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(first(x0, add(x1, x2))) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), add(x1, x2))) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), add(x1, x2))) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), add(x1, x2))) -> c19(A__FIRST(s(z0), a__add(mark(x1), mark(x2))))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2


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

(209) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) by 
   MARK(first(x0, dbl(x1))) -> c19(A__FIRST(mark(x0), dbl(mark(x1))), MARK(x0))
   MARK(first(x0, dbl(terms(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0))
   MARK(first(x0, dbl(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0))
   MARK(first(x0, dbl(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, dbl(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0))
   MARK(first(x0, dbl(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, dbl(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0))
   MARK(first(x0, dbl(recip(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0))
   MARK(first(x0, dbl(s(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(s(z0))), MARK(x0))
   MARK(first(x0, dbl(0))) -> c19(A__FIRST(mark(x0), a__dbl(0)), MARK(x0))
   MARK(first(x0, dbl(nil))) -> c19(A__FIRST(mark(x0), a__dbl(nil)), MARK(x0))
   MARK(first(terms(z0), dbl(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0)))
   MARK(first(sqr(z0), dbl(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0)))
   MARK(first(add(z0, z1), dbl(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1)))
   MARK(first(dbl(z0), dbl(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0)))
   MARK(first(first(z0, z1), dbl(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1)))
   MARK(first(cons(z0, z1), dbl(x1))) -> c19(A__FIRST(cons(mark(z0), z1), a__dbl(mark(x1))), MARK(cons(z0, z1)))
   MARK(first(recip(z0), dbl(x1))) -> c19(A__FIRST(recip(mark(z0)), a__dbl(mark(x1))), MARK(recip(z0)))
   MARK(first(s(z0), dbl(x1))) -> c19(A__FIRST(s(z0), a__dbl(mark(x1))), MARK(s(z0)))
   MARK(first(0, dbl(x1))) -> c19(A__FIRST(0, a__dbl(mark(x1))), MARK(0))
   MARK(first(nil, dbl(x1))) -> c19(A__FIRST(nil, a__dbl(mark(x1))), MARK(nil))

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

(210)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
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   MARK(first(x0, terms(x1))) -> c19(A__FIRST(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(first(x0, terms(terms(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(first(x0, terms(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(first(x0, terms(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, terms(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(first(x0, terms(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, terms(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(first(x0, terms(recip(z0)))) -> c19(A__FIRST(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(first(x0, terms(s(z0)))) -> c19(A__FIRST(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(first(x0, terms(0))) -> c19(A__FIRST(mark(x0), a__terms(0)), MARK(x0))
   MARK(first(x0, terms(nil))) -> c19(A__FIRST(mark(x0), a__terms(nil)), MARK(x0))
   MARK(first(terms(z0), terms(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(first(sqr(z0), terms(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(first(add(z0, z1), terms(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(first(dbl(z0), terms(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(first(first(z0, z1), terms(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(first(x0, terms(x1))) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), terms(x1))) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), terms(x1))) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), terms(x1))) -> c19(A__FIRST(s(z0), a__terms(mark(x1))))
   MARK(first(x0, sqr(terms(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(first(x0, sqr(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(first(x0, sqr(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, sqr(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(first(x0, sqr(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, sqr(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(first(x0, sqr(recip(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(first(x0, sqr(s(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(first(x0, sqr(0))) -> c19(A__FIRST(mark(x0), a__sqr(0)), MARK(x0))
   MARK(first(x0, sqr(nil))) -> c19(A__FIRST(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(first(terms(z0), sqr(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(first(sqr(z0), sqr(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(first(add(z0, z1), sqr(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(first(dbl(z0), sqr(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(first(first(z0, z1), sqr(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(first(x0, sqr(x1))) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), sqr(x1))) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), sqr(x1))) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), sqr(x1))) -> c19(A__FIRST(s(z0), a__sqr(mark(x1))))
   MARK(first(x0, add(x1, terms(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(first(x0, add(x1, sqr(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(first(x0, add(x1, add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, add(x1, dbl(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(first(x0, add(x1, first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, add(x1, cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(first(x0, add(x1, recip(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(first(x0, add(x1, s(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(first(x0, add(x1, 0))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(first(x0, add(x1, nil))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(first(x0, add(terms(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, add(sqr(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, add(add(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(first(x0, add(dbl(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, add(first(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(first(x0, add(cons(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(first(x0, add(recip(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, add(s(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(first(x0, add(0, x2))) -> c19(A__FIRST(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(first(x0, add(nil, x2))) -> c19(A__FIRST(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(first(terms(z0), add(x1, x2))) -> c19(A__FIRST(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(first(sqr(z0), add(x1, x2))) -> c19(A__FIRST(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(first(add(z0, z1), add(x1, x2))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(first(dbl(z0), add(x1, x2))) -> c19(A__FIRST(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(first(first(z0, z1), add(x1, x2))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(first(x0, add(x1, x2))) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), add(x1, x2))) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), add(x1, x2))) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), add(x1, x2))) -> c19(A__FIRST(s(z0), a__add(mark(x1), mark(x2))))
   MARK(first(x0, dbl(x1))) -> c19(A__FIRST(mark(x0), dbl(mark(x1))), MARK(x0))
   MARK(first(x0, dbl(terms(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0))
   MARK(first(x0, dbl(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0))
   MARK(first(x0, dbl(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, dbl(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0))
   MARK(first(x0, dbl(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, dbl(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0))
   MARK(first(x0, dbl(recip(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0))
   MARK(first(x0, dbl(s(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(s(z0))), MARK(x0))
   MARK(first(x0, dbl(0))) -> c19(A__FIRST(mark(x0), a__dbl(0)), MARK(x0))
   MARK(first(x0, dbl(nil))) -> c19(A__FIRST(mark(x0), a__dbl(nil)), MARK(x0))
   MARK(first(terms(z0), dbl(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0)))
   MARK(first(sqr(z0), dbl(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0)))
   MARK(first(add(z0, z1), dbl(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1)))
   MARK(first(dbl(z0), dbl(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0)))
   MARK(first(first(z0, z1), dbl(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1)))
   MARK(first(cons(z0, z1), dbl(x1))) -> c19(A__FIRST(cons(mark(z0), z1), a__dbl(mark(x1))), MARK(cons(z0, z1)))
   MARK(first(recip(z0), dbl(x1))) -> c19(A__FIRST(recip(mark(z0)), a__dbl(mark(x1))), MARK(recip(z0)))
   MARK(first(s(z0), dbl(x1))) -> c19(A__FIRST(s(z0), a__dbl(mark(x1))), MARK(s(z0)))
   MARK(first(0, dbl(x1))) -> c19(A__FIRST(0, a__dbl(mark(x1))), MARK(0))
   MARK(first(nil, dbl(x1))) -> c19(A__FIRST(nil, a__dbl(mark(x1))), MARK(nil))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
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   MARK(add(first(dbl(z0), x1), x2)) -> c17(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(first(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(recip(z0), x1), x2)) -> c17(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(s(z0), x1), x2)) -> c17(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(0, x1), x2)) -> c17(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(nil, x1), x2)) -> c17(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(x0, x1), s(z0))) -> c17(A__ADD(a__first(mark(x0), mark(x1)), s(z0)))
   MARK(add(first(x0, x1), 0)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), 0))
   MARK(add(first(x0, x1), nil)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), nil))
   MARK(add(first(x0, x1), x2)) -> c17(MARK(x2))
   MARK(add(0, s(x1))) -> c17(A__ADD(0, s(x1)))
   MARK(add(0, 0)) -> c17(A__ADD(0, 0))
   MARK(add(0, nil)) -> c17(A__ADD(0, nil))
   MARK(first(x0, terms(x1))) -> c19(A__FIRST(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(first(x0, terms(terms(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(first(x0, terms(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(first(x0, terms(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, terms(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(first(x0, terms(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, terms(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(first(x0, terms(recip(z0)))) -> c19(A__FIRST(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(first(x0, terms(s(z0)))) -> c19(A__FIRST(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(first(x0, terms(0))) -> c19(A__FIRST(mark(x0), a__terms(0)), MARK(x0))
   MARK(first(x0, terms(nil))) -> c19(A__FIRST(mark(x0), a__terms(nil)), MARK(x0))
   MARK(first(terms(z0), terms(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(first(sqr(z0), terms(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(first(add(z0, z1), terms(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(first(dbl(z0), terms(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(first(first(z0, z1), terms(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(first(x0, terms(x1))) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), terms(x1))) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), terms(x1))) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), terms(x1))) -> c19(A__FIRST(s(z0), a__terms(mark(x1))))
   MARK(first(x0, sqr(terms(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(first(x0, sqr(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(first(x0, sqr(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, sqr(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(first(x0, sqr(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, sqr(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(first(x0, sqr(recip(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(first(x0, sqr(s(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(first(x0, sqr(0))) -> c19(A__FIRST(mark(x0), a__sqr(0)), MARK(x0))
   MARK(first(x0, sqr(nil))) -> c19(A__FIRST(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(first(terms(z0), sqr(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(first(sqr(z0), sqr(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(first(add(z0, z1), sqr(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(first(dbl(z0), sqr(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(first(first(z0, z1), sqr(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(first(x0, sqr(x1))) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), sqr(x1))) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), sqr(x1))) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), sqr(x1))) -> c19(A__FIRST(s(z0), a__sqr(mark(x1))))
   MARK(first(x0, add(x1, terms(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(first(x0, add(x1, sqr(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(first(x0, add(x1, add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, add(x1, dbl(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(first(x0, add(x1, first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, add(x1, cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(first(x0, add(x1, recip(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(first(x0, add(x1, s(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(first(x0, add(x1, 0))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(first(x0, add(x1, nil))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(first(x0, add(terms(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, add(sqr(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, add(add(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(first(x0, add(dbl(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, add(first(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(first(x0, add(cons(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(first(x0, add(recip(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, add(s(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(first(x0, add(0, x2))) -> c19(A__FIRST(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(first(x0, add(nil, x2))) -> c19(A__FIRST(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(first(terms(z0), add(x1, x2))) -> c19(A__FIRST(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(first(sqr(z0), add(x1, x2))) -> c19(A__FIRST(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(first(add(z0, z1), add(x1, x2))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(first(dbl(z0), add(x1, x2))) -> c19(A__FIRST(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(first(first(z0, z1), add(x1, x2))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(first(x0, add(x1, x2))) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), add(x1, x2))) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), add(x1, x2))) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), add(x1, x2))) -> c19(A__FIRST(s(z0), a__add(mark(x1), mark(x2))))
   MARK(first(x0, dbl(x1))) -> c19(A__FIRST(mark(x0), dbl(mark(x1))), MARK(x0))
   MARK(first(x0, dbl(terms(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0))
   MARK(first(x0, dbl(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0))
   MARK(first(x0, dbl(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, dbl(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0))
   MARK(first(x0, dbl(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, dbl(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0))
   MARK(first(x0, dbl(recip(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0))
   MARK(first(x0, dbl(s(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(s(z0))), MARK(x0))
   MARK(first(x0, dbl(0))) -> c19(A__FIRST(mark(x0), a__dbl(0)), MARK(x0))
   MARK(first(x0, dbl(nil))) -> c19(A__FIRST(mark(x0), a__dbl(nil)), MARK(x0))
   MARK(first(terms(z0), dbl(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0)))
   MARK(first(sqr(z0), dbl(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0)))
   MARK(first(add(z0, z1), dbl(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1)))
   MARK(first(dbl(z0), dbl(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0)))
   MARK(first(first(z0, z1), dbl(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1)))
   MARK(first(cons(z0, z1), dbl(x1))) -> c19(A__FIRST(cons(mark(z0), z1), a__dbl(mark(x1))), MARK(cons(z0, z1)))
   MARK(first(recip(z0), dbl(x1))) -> c19(A__FIRST(recip(mark(z0)), a__dbl(mark(x1))), MARK(recip(z0)))
   MARK(first(s(z0), dbl(x1))) -> c19(A__FIRST(s(z0), a__dbl(mark(x1))), MARK(s(z0)))
   MARK(first(0, dbl(x1))) -> c19(A__FIRST(0, a__dbl(mark(x1))), MARK(0))
   MARK(first(nil, dbl(x1))) -> c19(A__FIRST(nil, a__dbl(mark(x1))), MARK(nil))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2


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

(211) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing nodes:
   MARK(first(0, dbl(x1))) -> c19(A__FIRST(0, a__dbl(mark(x1))), MARK(0))
   MARK(first(nil, dbl(x1))) -> c19(A__FIRST(nil, a__dbl(mark(x1))), MARK(nil))

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

(212)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
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   MARK(add(dbl(terms(z0)), x1)) -> c17(A__ADD(a__dbl(a__terms(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(sqr(z0)), x1)) -> c17(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(add(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(dbl(dbl(z0)), x1)) -> c17(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(first(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(dbl(cons(z0, z1)), x1)) -> c17(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(recip(z0)), x1)) -> c17(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(s(z0)), x1)) -> c17(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(x1))
   MARK(add(dbl(0), x1)) -> c17(A__ADD(a__dbl(0), mark(x1)), MARK(x1))
   MARK(add(dbl(nil), x1)) -> c17(A__ADD(a__dbl(nil), mark(x1)), MARK(x1))
   MARK(add(dbl(x0), s(z0))) -> c17(A__ADD(a__dbl(mark(x0)), s(z0)))
   MARK(add(dbl(x0), 0)) -> c17(A__ADD(a__dbl(mark(x0)), 0))
   MARK(add(dbl(x0), nil)) -> c17(A__ADD(a__dbl(mark(x0)), nil))
   MARK(add(dbl(x0), x1)) -> c17(MARK(x1))
   MARK(add(first(x0, terms(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, sqr(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   MARK(add(first(x0, dbl(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   MARK(add(first(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2))
   MARK(add(first(x0, recip(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, s(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(x2))
   MARK(add(first(x0, 0), x2)) -> c17(A__ADD(a__first(mark(x0), 0), mark(x2)), MARK(x2))
   MARK(add(first(x0, nil), x2)) -> c17(A__ADD(a__first(mark(x0), nil), mark(x2)), MARK(x2))
   MARK(add(first(terms(z0), x1), x2)) -> c17(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(sqr(z0), x1), x2)) -> c17(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(add(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(dbl(z0), x1), x2)) -> c17(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(first(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(recip(z0), x1), x2)) -> c17(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(s(z0), x1), x2)) -> c17(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(0, x1), x2)) -> c17(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(nil, x1), x2)) -> c17(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(x0, x1), s(z0))) -> c17(A__ADD(a__first(mark(x0), mark(x1)), s(z0)))
   MARK(add(first(x0, x1), 0)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), 0))
   MARK(add(first(x0, x1), nil)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), nil))
   MARK(add(first(x0, x1), x2)) -> c17(MARK(x2))
   MARK(add(0, s(x1))) -> c17(A__ADD(0, s(x1)))
   MARK(add(0, 0)) -> c17(A__ADD(0, 0))
   MARK(add(0, nil)) -> c17(A__ADD(0, nil))
   MARK(first(x0, terms(x1))) -> c19(A__FIRST(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(first(x0, terms(terms(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(first(x0, terms(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(first(x0, terms(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, terms(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(first(x0, terms(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, terms(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(first(x0, terms(recip(z0)))) -> c19(A__FIRST(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(first(x0, terms(s(z0)))) -> c19(A__FIRST(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(first(x0, terms(0))) -> c19(A__FIRST(mark(x0), a__terms(0)), MARK(x0))
   MARK(first(x0, terms(nil))) -> c19(A__FIRST(mark(x0), a__terms(nil)), MARK(x0))
   MARK(first(terms(z0), terms(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(first(sqr(z0), terms(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(first(add(z0, z1), terms(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(first(dbl(z0), terms(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(first(first(z0, z1), terms(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(first(x0, terms(x1))) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), terms(x1))) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), terms(x1))) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), terms(x1))) -> c19(A__FIRST(s(z0), a__terms(mark(x1))))
   MARK(first(x0, sqr(terms(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(first(x0, sqr(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(first(x0, sqr(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, sqr(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(first(x0, sqr(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, sqr(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(first(x0, sqr(recip(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(first(x0, sqr(s(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(first(x0, sqr(0))) -> c19(A__FIRST(mark(x0), a__sqr(0)), MARK(x0))
   MARK(first(x0, sqr(nil))) -> c19(A__FIRST(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(first(terms(z0), sqr(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(first(sqr(z0), sqr(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(first(add(z0, z1), sqr(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(first(dbl(z0), sqr(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(first(first(z0, z1), sqr(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(first(x0, sqr(x1))) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), sqr(x1))) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), sqr(x1))) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), sqr(x1))) -> c19(A__FIRST(s(z0), a__sqr(mark(x1))))
   MARK(first(x0, add(x1, terms(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(first(x0, add(x1, sqr(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(first(x0, add(x1, add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, add(x1, dbl(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(first(x0, add(x1, first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, add(x1, cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(first(x0, add(x1, recip(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(first(x0, add(x1, s(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(first(x0, add(x1, 0))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(first(x0, add(x1, nil))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(first(x0, add(terms(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, add(sqr(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, add(add(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(first(x0, add(dbl(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, add(first(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(first(x0, add(cons(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(first(x0, add(recip(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, add(s(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(first(x0, add(0, x2))) -> c19(A__FIRST(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(first(x0, add(nil, x2))) -> c19(A__FIRST(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(first(terms(z0), add(x1, x2))) -> c19(A__FIRST(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(first(sqr(z0), add(x1, x2))) -> c19(A__FIRST(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(first(add(z0, z1), add(x1, x2))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(first(dbl(z0), add(x1, x2))) -> c19(A__FIRST(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(first(first(z0, z1), add(x1, x2))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(first(x0, add(x1, x2))) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), add(x1, x2))) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), add(x1, x2))) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), add(x1, x2))) -> c19(A__FIRST(s(z0), a__add(mark(x1), mark(x2))))
   MARK(first(x0, dbl(x1))) -> c19(A__FIRST(mark(x0), dbl(mark(x1))), MARK(x0))
   MARK(first(x0, dbl(terms(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0))
   MARK(first(x0, dbl(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0))
   MARK(first(x0, dbl(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, dbl(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0))
   MARK(first(x0, dbl(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, dbl(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0))
   MARK(first(x0, dbl(recip(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0))
   MARK(first(x0, dbl(s(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(s(z0))), MARK(x0))
   MARK(first(x0, dbl(0))) -> c19(A__FIRST(mark(x0), a__dbl(0)), MARK(x0))
   MARK(first(x0, dbl(nil))) -> c19(A__FIRST(mark(x0), a__dbl(nil)), MARK(x0))
   MARK(first(terms(z0), dbl(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0)))
   MARK(first(sqr(z0), dbl(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0)))
   MARK(first(add(z0, z1), dbl(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1)))
   MARK(first(dbl(z0), dbl(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0)))
   MARK(first(first(z0, z1), dbl(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1)))
   MARK(first(cons(z0, z1), dbl(x1))) -> c19(A__FIRST(cons(mark(z0), z1), a__dbl(mark(x1))), MARK(cons(z0, z1)))
   MARK(first(recip(z0), dbl(x1))) -> c19(A__FIRST(recip(mark(z0)), a__dbl(mark(x1))), MARK(recip(z0)))
   MARK(first(s(z0), dbl(x1))) -> c19(A__FIRST(s(z0), a__dbl(mark(x1))), MARK(s(z0)))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
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   MARK(add(add(first(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(recip(z0), x1), x2)) -> c17(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(s(z0), x1), x2)) -> c17(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(0, x1), x2)) -> c17(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(nil, x1), x2)) -> c17(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(add(x0, x1), s(z0))) -> c17(A__ADD(a__add(mark(x0), mark(x1)), s(z0)))
   MARK(add(add(x0, x1), 0)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), 0))
   MARK(add(add(x0, x1), nil)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), nil))
   MARK(add(add(x0, x1), x2)) -> c17(MARK(x2))
   MARK(add(dbl(terms(z0)), x1)) -> c17(A__ADD(a__dbl(a__terms(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(sqr(z0)), x1)) -> c17(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(add(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(dbl(dbl(z0)), x1)) -> c17(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(first(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   MARK(add(dbl(cons(z0, z1)), x1)) -> c17(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(x1))
   MARK(add(dbl(recip(z0)), x1)) -> c17(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(x1))
   MARK(add(dbl(s(z0)), x1)) -> c17(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(x1))
   MARK(add(dbl(0), x1)) -> c17(A__ADD(a__dbl(0), mark(x1)), MARK(x1))
   MARK(add(dbl(nil), x1)) -> c17(A__ADD(a__dbl(nil), mark(x1)), MARK(x1))
   MARK(add(dbl(x0), s(z0))) -> c17(A__ADD(a__dbl(mark(x0)), s(z0)))
   MARK(add(dbl(x0), 0)) -> c17(A__ADD(a__dbl(mark(x0)), 0))
   MARK(add(dbl(x0), nil)) -> c17(A__ADD(a__dbl(mark(x0)), nil))
   MARK(add(dbl(x0), x1)) -> c17(MARK(x1))
   MARK(add(first(x0, terms(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, sqr(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   MARK(add(first(x0, dbl(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   MARK(add(first(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2))
   MARK(add(first(x0, recip(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, s(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(x2))
   MARK(add(first(x0, 0), x2)) -> c17(A__ADD(a__first(mark(x0), 0), mark(x2)), MARK(x2))
   MARK(add(first(x0, nil), x2)) -> c17(A__ADD(a__first(mark(x0), nil), mark(x2)), MARK(x2))
   MARK(add(first(terms(z0), x1), x2)) -> c17(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(sqr(z0), x1), x2)) -> c17(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(add(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(dbl(z0), x1), x2)) -> c17(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(first(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(recip(z0), x1), x2)) -> c17(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(s(z0), x1), x2)) -> c17(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(0, x1), x2)) -> c17(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(nil, x1), x2)) -> c17(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(x0, x1), s(z0))) -> c17(A__ADD(a__first(mark(x0), mark(x1)), s(z0)))
   MARK(add(first(x0, x1), 0)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), 0))
   MARK(add(first(x0, x1), nil)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), nil))
   MARK(add(first(x0, x1), x2)) -> c17(MARK(x2))
   MARK(add(0, s(x1))) -> c17(A__ADD(0, s(x1)))
   MARK(add(0, 0)) -> c17(A__ADD(0, 0))
   MARK(add(0, nil)) -> c17(A__ADD(0, nil))
   MARK(first(x0, terms(x1))) -> c19(A__FIRST(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(first(x0, terms(terms(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(first(x0, terms(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(first(x0, terms(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, terms(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(first(x0, terms(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, terms(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(first(x0, terms(recip(z0)))) -> c19(A__FIRST(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(first(x0, terms(s(z0)))) -> c19(A__FIRST(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(first(x0, terms(0))) -> c19(A__FIRST(mark(x0), a__terms(0)), MARK(x0))
   MARK(first(x0, terms(nil))) -> c19(A__FIRST(mark(x0), a__terms(nil)), MARK(x0))
   MARK(first(terms(z0), terms(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(first(sqr(z0), terms(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(first(add(z0, z1), terms(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(first(dbl(z0), terms(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(first(first(z0, z1), terms(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(first(x0, terms(x1))) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), terms(x1))) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), terms(x1))) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), terms(x1))) -> c19(A__FIRST(s(z0), a__terms(mark(x1))))
   MARK(first(x0, sqr(terms(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(first(x0, sqr(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(first(x0, sqr(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, sqr(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(first(x0, sqr(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, sqr(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(first(x0, sqr(recip(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(first(x0, sqr(s(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(first(x0, sqr(0))) -> c19(A__FIRST(mark(x0), a__sqr(0)), MARK(x0))
   MARK(first(x0, sqr(nil))) -> c19(A__FIRST(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(first(terms(z0), sqr(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(first(sqr(z0), sqr(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(first(add(z0, z1), sqr(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(first(dbl(z0), sqr(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(first(first(z0, z1), sqr(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(first(x0, sqr(x1))) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), sqr(x1))) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), sqr(x1))) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), sqr(x1))) -> c19(A__FIRST(s(z0), a__sqr(mark(x1))))
   MARK(first(x0, add(x1, terms(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(first(x0, add(x1, sqr(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(first(x0, add(x1, add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, add(x1, dbl(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(first(x0, add(x1, first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, add(x1, cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(first(x0, add(x1, recip(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(first(x0, add(x1, s(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(first(x0, add(x1, 0))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(first(x0, add(x1, nil))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(first(x0, add(terms(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, add(sqr(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, add(add(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(first(x0, add(dbl(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, add(first(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(first(x0, add(cons(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(first(x0, add(recip(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, add(s(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(first(x0, add(0, x2))) -> c19(A__FIRST(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(first(x0, add(nil, x2))) -> c19(A__FIRST(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(first(terms(z0), add(x1, x2))) -> c19(A__FIRST(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(first(sqr(z0), add(x1, x2))) -> c19(A__FIRST(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(first(add(z0, z1), add(x1, x2))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(first(dbl(z0), add(x1, x2))) -> c19(A__FIRST(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(first(first(z0, z1), add(x1, x2))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(first(x0, add(x1, x2))) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), add(x1, x2))) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), add(x1, x2))) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), add(x1, x2))) -> c19(A__FIRST(s(z0), a__add(mark(x1), mark(x2))))
   MARK(first(x0, dbl(x1))) -> c19(A__FIRST(mark(x0), dbl(mark(x1))), MARK(x0))
   MARK(first(x0, dbl(terms(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0))
   MARK(first(x0, dbl(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0))
   MARK(first(x0, dbl(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, dbl(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0))
   MARK(first(x0, dbl(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, dbl(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0))
   MARK(first(x0, dbl(recip(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0))
   MARK(first(x0, dbl(s(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(s(z0))), MARK(x0))
   MARK(first(x0, dbl(0))) -> c19(A__FIRST(mark(x0), a__dbl(0)), MARK(x0))
   MARK(first(x0, dbl(nil))) -> c19(A__FIRST(mark(x0), a__dbl(nil)), MARK(x0))
   MARK(first(terms(z0), dbl(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0)))
   MARK(first(sqr(z0), dbl(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0)))
   MARK(first(add(z0, z1), dbl(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1)))
   MARK(first(dbl(z0), dbl(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0)))
   MARK(first(first(z0, z1), dbl(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1)))
   MARK(first(cons(z0, z1), dbl(x1))) -> c19(A__FIRST(cons(mark(z0), z1), a__dbl(mark(x1))), MARK(cons(z0, z1)))
   MARK(first(recip(z0), dbl(x1))) -> c19(A__FIRST(recip(mark(z0)), a__dbl(mark(x1))), MARK(recip(z0)))
   MARK(first(s(z0), dbl(x1))) -> c19(A__FIRST(s(z0), a__dbl(mark(x1))), MARK(s(z0)))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2


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

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

(214)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
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   MARK(first(s(z0), dbl(x1))) -> c19(A__FIRST(s(z0), a__dbl(mark(x1))))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2))))
   MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0))
   MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0))
   MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0))
   MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0))
   MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1))))
   MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0))
   MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0))
   MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0))
   MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2))))
   MARK(add(x0, cons(terms(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(sqr(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0))
   MARK(add(x0, cons(dbl(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0))
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   MARK(first(x0, dbl(s(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(s(z0))), MARK(x0))
   MARK(first(x0, dbl(0))) -> c19(A__FIRST(mark(x0), a__dbl(0)), MARK(x0))
   MARK(first(x0, dbl(nil))) -> c19(A__FIRST(mark(x0), a__dbl(nil)), MARK(x0))
   MARK(first(terms(z0), dbl(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0)))
   MARK(first(sqr(z0), dbl(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0)))
   MARK(first(add(z0, z1), dbl(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1)))
   MARK(first(dbl(z0), dbl(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0)))
   MARK(first(first(z0, z1), dbl(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1)))
   MARK(first(x0, dbl(x1))) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), dbl(x1))) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), dbl(x1))) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), dbl(x1))) -> c19(A__FIRST(s(z0), a__dbl(mark(x1))))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2


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

(215) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) by 
   MARK(first(x0, first(x1, x2))) -> c19(A__FIRST(mark(x0), first(mark(x1), mark(x2))), MARK(x0))
   MARK(first(x0, first(x1, terms(z0)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(first(x0, first(x1, sqr(z0)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(first(x0, first(x1, add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, first(x1, dbl(z0)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(first(x0, first(x1, first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, first(x1, cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(first(x0, first(x1, recip(z0)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(first(x0, first(x1, s(z0)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), s(z0))), MARK(x0))
   MARK(first(x0, first(x1, 0))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0))
   MARK(first(x0, first(x1, nil))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0))
   MARK(first(x0, first(terms(z0), x2))) -> c19(A__FIRST(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, first(sqr(z0), x2))) -> c19(A__FIRST(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, first(add(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(first(x0, first(dbl(z0), x2))) -> c19(A__FIRST(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, first(first(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(first(x0, first(cons(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(first(x0, first(recip(z0), x2))) -> c19(A__FIRST(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, first(s(z0), x2))) -> c19(A__FIRST(mark(x0), a__first(s(z0), mark(x2))), MARK(x0))
   MARK(first(x0, first(0, x2))) -> c19(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0))
   MARK(first(x0, first(nil, x2))) -> c19(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0))
   MARK(first(terms(z0), first(x1, x2))) -> c19(A__FIRST(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(first(sqr(z0), first(x1, x2))) -> c19(A__FIRST(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(first(add(z0, z1), first(x1, x2))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(first(dbl(z0), first(x1, x2))) -> c19(A__FIRST(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(first(first(z0, z1), first(x1, x2))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(first(cons(z0, z1), first(x1, x2))) -> c19(A__FIRST(cons(mark(z0), z1), a__first(mark(x1), mark(x2))), MARK(cons(z0, z1)))
   MARK(first(recip(z0), first(x1, x2))) -> c19(A__FIRST(recip(mark(z0)), a__first(mark(x1), mark(x2))), MARK(recip(z0)))
   MARK(first(s(z0), first(x1, x2))) -> c19(A__FIRST(s(z0), a__first(mark(x1), mark(x2))), MARK(s(z0)))
   MARK(first(0, first(x1, x2))) -> c19(A__FIRST(0, a__first(mark(x1), mark(x2))), MARK(0))
   MARK(first(nil, first(x1, x2))) -> c19(A__FIRST(nil, a__first(mark(x1), mark(x2))), MARK(nil))

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

(216)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
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   MARK(first(x0, sqr(terms(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(first(x0, sqr(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(first(x0, sqr(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, sqr(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(first(x0, sqr(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, sqr(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(first(x0, sqr(recip(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(first(x0, sqr(s(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(first(x0, sqr(0))) -> c19(A__FIRST(mark(x0), a__sqr(0)), MARK(x0))
   MARK(first(x0, sqr(nil))) -> c19(A__FIRST(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(first(terms(z0), sqr(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(first(sqr(z0), sqr(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(first(add(z0, z1), sqr(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(first(dbl(z0), sqr(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(first(first(z0, z1), sqr(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(first(x0, sqr(x1))) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), sqr(x1))) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), sqr(x1))) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), sqr(x1))) -> c19(A__FIRST(s(z0), a__sqr(mark(x1))))
   MARK(first(x0, add(x1, terms(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(first(x0, add(x1, sqr(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(first(x0, add(x1, add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, add(x1, dbl(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(first(x0, add(x1, first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, add(x1, cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(first(x0, add(x1, recip(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(first(x0, add(x1, s(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(first(x0, add(x1, 0))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(first(x0, add(x1, nil))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(first(x0, add(terms(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, add(sqr(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, add(add(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(first(x0, add(dbl(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, add(first(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(first(x0, add(cons(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(first(x0, add(recip(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, add(s(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(first(x0, add(0, x2))) -> c19(A__FIRST(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(first(x0, add(nil, x2))) -> c19(A__FIRST(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(first(terms(z0), add(x1, x2))) -> c19(A__FIRST(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(first(sqr(z0), add(x1, x2))) -> c19(A__FIRST(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(first(add(z0, z1), add(x1, x2))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(first(dbl(z0), add(x1, x2))) -> c19(A__FIRST(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(first(first(z0, z1), add(x1, x2))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(first(x0, add(x1, x2))) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), add(x1, x2))) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), add(x1, x2))) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), add(x1, x2))) -> c19(A__FIRST(s(z0), a__add(mark(x1), mark(x2))))
   MARK(first(x0, dbl(terms(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0))
   MARK(first(x0, dbl(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0))
   MARK(first(x0, dbl(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, dbl(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0))
   MARK(first(x0, dbl(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, dbl(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0))
   MARK(first(x0, dbl(recip(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0))
   MARK(first(x0, dbl(s(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(s(z0))), MARK(x0))
   MARK(first(x0, dbl(0))) -> c19(A__FIRST(mark(x0), a__dbl(0)), MARK(x0))
   MARK(first(x0, dbl(nil))) -> c19(A__FIRST(mark(x0), a__dbl(nil)), MARK(x0))
   MARK(first(terms(z0), dbl(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0)))
   MARK(first(sqr(z0), dbl(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0)))
   MARK(first(add(z0, z1), dbl(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1)))
   MARK(first(dbl(z0), dbl(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0)))
   MARK(first(first(z0, z1), dbl(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1)))
   MARK(first(x0, dbl(x1))) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), dbl(x1))) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), dbl(x1))) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), dbl(x1))) -> c19(A__FIRST(s(z0), a__dbl(mark(x1))))
   MARK(first(x0, first(x1, x2))) -> c19(A__FIRST(mark(x0), first(mark(x1), mark(x2))), MARK(x0))
   MARK(first(x0, first(x1, terms(z0)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(first(x0, first(x1, sqr(z0)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(first(x0, first(x1, add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, first(x1, dbl(z0)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(first(x0, first(x1, first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, first(x1, cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(first(x0, first(x1, recip(z0)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(first(x0, first(x1, s(z0)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), s(z0))), MARK(x0))
   MARK(first(x0, first(x1, 0))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0))
   MARK(first(x0, first(x1, nil))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0))
   MARK(first(x0, first(terms(z0), x2))) -> c19(A__FIRST(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, first(sqr(z0), x2))) -> c19(A__FIRST(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, first(add(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(first(x0, first(dbl(z0), x2))) -> c19(A__FIRST(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, first(first(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(first(x0, first(cons(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(first(x0, first(recip(z0), x2))) -> c19(A__FIRST(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, first(s(z0), x2))) -> c19(A__FIRST(mark(x0), a__first(s(z0), mark(x2))), MARK(x0))
   MARK(first(x0, first(0, x2))) -> c19(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0))
   MARK(first(x0, first(nil, x2))) -> c19(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0))
   MARK(first(terms(z0), first(x1, x2))) -> c19(A__FIRST(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(first(sqr(z0), first(x1, x2))) -> c19(A__FIRST(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(first(add(z0, z1), first(x1, x2))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(first(dbl(z0), first(x1, x2))) -> c19(A__FIRST(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(first(first(z0, z1), first(x1, x2))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(first(cons(z0, z1), first(x1, x2))) -> c19(A__FIRST(cons(mark(z0), z1), a__first(mark(x1), mark(x2))), MARK(cons(z0, z1)))
   MARK(first(recip(z0), first(x1, x2))) -> c19(A__FIRST(recip(mark(z0)), a__first(mark(x1), mark(x2))), MARK(recip(z0)))
   MARK(first(s(z0), first(x1, x2))) -> c19(A__FIRST(s(z0), a__first(mark(x1), mark(x2))), MARK(s(z0)))
   MARK(first(0, first(x1, x2))) -> c19(A__FIRST(0, a__first(mark(x1), mark(x2))), MARK(0))
   MARK(first(nil, first(x1, x2))) -> c19(A__FIRST(nil, a__first(mark(x1), mark(x2))), MARK(nil))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
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   MARK(add(first(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2))
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   MARK(add(first(sqr(z0), x1), x2)) -> c17(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(add(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
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   MARK(add(first(recip(z0), x1), x2)) -> c17(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(s(z0), x1), x2)) -> c17(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(0, x1), x2)) -> c17(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(x2))
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   MARK(add(first(x0, x1), s(z0))) -> c17(A__ADD(a__first(mark(x0), mark(x1)), s(z0)))
   MARK(add(first(x0, x1), 0)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), 0))
   MARK(add(first(x0, x1), nil)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), nil))
   MARK(add(first(x0, x1), x2)) -> c17(MARK(x2))
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   MARK(add(0, 0)) -> c17(A__ADD(0, 0))
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   MARK(first(x0, terms(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(first(x0, terms(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
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   MARK(first(x0, terms(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, terms(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(first(x0, terms(recip(z0)))) -> c19(A__FIRST(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(first(x0, terms(s(z0)))) -> c19(A__FIRST(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(first(x0, terms(0))) -> c19(A__FIRST(mark(x0), a__terms(0)), MARK(x0))
   MARK(first(x0, terms(nil))) -> c19(A__FIRST(mark(x0), a__terms(nil)), MARK(x0))
   MARK(first(terms(z0), terms(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
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   MARK(first(add(z0, z1), terms(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(first(dbl(z0), terms(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(first(first(z0, z1), terms(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
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   MARK(first(cons(z0, z1), terms(x1))) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), terms(x1))) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), terms(x1))) -> c19(A__FIRST(s(z0), a__terms(mark(x1))))
   MARK(first(x0, sqr(terms(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(first(x0, sqr(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(first(x0, sqr(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
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   MARK(first(x0, sqr(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, sqr(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
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   MARK(first(cons(z0, z1), sqr(x1))) -> c19(MARK(cons(z0, z1)))
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   MARK(first(s(z0), sqr(x1))) -> c19(A__FIRST(s(z0), a__sqr(mark(x1))))
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   MARK(first(x0, add(x1, sqr(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
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   MARK(first(x0, add(x1, s(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
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   MARK(first(x0, add(sqr(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, add(add(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
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   MARK(first(x0, add(first(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(first(x0, add(cons(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
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   MARK(first(x0, add(s(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(first(x0, add(0, x2))) -> c19(A__FIRST(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(first(x0, add(nil, x2))) -> c19(A__FIRST(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(first(terms(z0), add(x1, x2))) -> c19(A__FIRST(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(first(sqr(z0), add(x1, x2))) -> c19(A__FIRST(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(first(add(z0, z1), add(x1, x2))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(first(dbl(z0), add(x1, x2))) -> c19(A__FIRST(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(first(first(z0, z1), add(x1, x2))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(first(x0, add(x1, x2))) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), add(x1, x2))) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), add(x1, x2))) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), add(x1, x2))) -> c19(A__FIRST(s(z0), a__add(mark(x1), mark(x2))))
   MARK(first(x0, dbl(terms(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0))
   MARK(first(x0, dbl(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0))
   MARK(first(x0, dbl(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, dbl(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0))
   MARK(first(x0, dbl(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, dbl(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0))
   MARK(first(x0, dbl(recip(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0))
   MARK(first(x0, dbl(s(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(s(z0))), MARK(x0))
   MARK(first(x0, dbl(0))) -> c19(A__FIRST(mark(x0), a__dbl(0)), MARK(x0))
   MARK(first(x0, dbl(nil))) -> c19(A__FIRST(mark(x0), a__dbl(nil)), MARK(x0))
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   MARK(first(sqr(z0), dbl(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0)))
   MARK(first(add(z0, z1), dbl(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1)))
   MARK(first(dbl(z0), dbl(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0)))
   MARK(first(first(z0, z1), dbl(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1)))
   MARK(first(x0, dbl(x1))) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), dbl(x1))) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), dbl(x1))) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), dbl(x1))) -> c19(A__FIRST(s(z0), a__dbl(mark(x1))))
   MARK(first(x0, first(x1, x2))) -> c19(A__FIRST(mark(x0), first(mark(x1), mark(x2))), MARK(x0))
   MARK(first(x0, first(x1, terms(z0)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(first(x0, first(x1, sqr(z0)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(first(x0, first(x1, add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
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   MARK(first(x0, first(x1, first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, first(x1, cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0))
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   MARK(first(x0, first(x1, s(z0)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), s(z0))), MARK(x0))
   MARK(first(x0, first(x1, 0))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0))
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   MARK(first(x0, first(sqr(z0), x2))) -> c19(A__FIRST(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, first(add(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
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   MARK(first(x0, first(first(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
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   MARK(first(x0, first(recip(z0), x2))) -> c19(A__FIRST(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, first(s(z0), x2))) -> c19(A__FIRST(mark(x0), a__first(s(z0), mark(x2))), MARK(x0))
   MARK(first(x0, first(0, x2))) -> c19(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0))
   MARK(first(x0, first(nil, x2))) -> c19(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0))
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   MARK(first(sqr(z0), first(x1, x2))) -> c19(A__FIRST(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(first(add(z0, z1), first(x1, x2))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(first(dbl(z0), first(x1, x2))) -> c19(A__FIRST(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(first(first(z0, z1), first(x1, x2))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(first(cons(z0, z1), first(x1, x2))) -> c19(A__FIRST(cons(mark(z0), z1), a__first(mark(x1), mark(x2))), MARK(cons(z0, z1)))
   MARK(first(recip(z0), first(x1, x2))) -> c19(A__FIRST(recip(mark(z0)), a__first(mark(x1), mark(x2))), MARK(recip(z0)))
   MARK(first(s(z0), first(x1, x2))) -> c19(A__FIRST(s(z0), a__first(mark(x1), mark(x2))), MARK(s(z0)))
   MARK(first(0, first(x1, x2))) -> c19(A__FIRST(0, a__first(mark(x1), mark(x2))), MARK(0))
   MARK(first(nil, first(x1, x2))) -> c19(A__FIRST(nil, a__first(mark(x1), mark(x2))), MARK(nil))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2


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

(217) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing nodes:
   MARK(first(nil, first(x1, x2))) -> c19(A__FIRST(nil, a__first(mark(x1), mark(x2))), MARK(nil))
   MARK(first(0, first(x1, x2))) -> c19(A__FIRST(0, a__first(mark(x1), mark(x2))), MARK(0))

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

(218)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2))))
   MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0))
   MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0))
   MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0))
   MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0))
   MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1))))
   MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0))
   MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0))
   MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0))
   MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2))))
   MARK(add(x0, cons(terms(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(sqr(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0))
   MARK(add(x0, cons(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0))
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   MARK(first(x0, dbl(recip(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0))
   MARK(first(x0, dbl(s(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(s(z0))), MARK(x0))
   MARK(first(x0, dbl(0))) -> c19(A__FIRST(mark(x0), a__dbl(0)), MARK(x0))
   MARK(first(x0, dbl(nil))) -> c19(A__FIRST(mark(x0), a__dbl(nil)), MARK(x0))
   MARK(first(terms(z0), dbl(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0)))
   MARK(first(sqr(z0), dbl(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0)))
   MARK(first(add(z0, z1), dbl(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1)))
   MARK(first(dbl(z0), dbl(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0)))
   MARK(first(first(z0, z1), dbl(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1)))
   MARK(first(x0, dbl(x1))) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), dbl(x1))) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), dbl(x1))) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), dbl(x1))) -> c19(A__FIRST(s(z0), a__dbl(mark(x1))))
   MARK(first(x0, first(x1, x2))) -> c19(A__FIRST(mark(x0), first(mark(x1), mark(x2))), MARK(x0))
   MARK(first(x0, first(x1, terms(z0)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(first(x0, first(x1, sqr(z0)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(first(x0, first(x1, add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, first(x1, dbl(z0)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(first(x0, first(x1, first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, first(x1, cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(first(x0, first(x1, recip(z0)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(first(x0, first(x1, s(z0)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), s(z0))), MARK(x0))
   MARK(first(x0, first(x1, 0))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0))
   MARK(first(x0, first(x1, nil))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0))
   MARK(first(x0, first(terms(z0), x2))) -> c19(A__FIRST(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, first(sqr(z0), x2))) -> c19(A__FIRST(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, first(add(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(first(x0, first(dbl(z0), x2))) -> c19(A__FIRST(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, first(first(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(first(x0, first(cons(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(first(x0, first(recip(z0), x2))) -> c19(A__FIRST(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, first(s(z0), x2))) -> c19(A__FIRST(mark(x0), a__first(s(z0), mark(x2))), MARK(x0))
   MARK(first(x0, first(0, x2))) -> c19(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0))
   MARK(first(x0, first(nil, x2))) -> c19(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0))
   MARK(first(terms(z0), first(x1, x2))) -> c19(A__FIRST(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(first(sqr(z0), first(x1, x2))) -> c19(A__FIRST(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(first(add(z0, z1), first(x1, x2))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(first(dbl(z0), first(x1, x2))) -> c19(A__FIRST(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(first(first(z0, z1), first(x1, x2))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(first(cons(z0, z1), first(x1, x2))) -> c19(A__FIRST(cons(mark(z0), z1), a__first(mark(x1), mark(x2))), MARK(cons(z0, z1)))
   MARK(first(recip(z0), first(x1, x2))) -> c19(A__FIRST(recip(mark(z0)), a__first(mark(x1), mark(x2))), MARK(recip(z0)))
   MARK(first(s(z0), first(x1, x2))) -> c19(A__FIRST(s(z0), a__first(mark(x1), mark(x2))), MARK(s(z0)))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2))))
   MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0))
   MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0))
   MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0))
   MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0))
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   MARK(first(add(z0, z1), sqr(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(first(dbl(z0), sqr(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(first(first(z0, z1), sqr(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(first(x0, sqr(x1))) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), sqr(x1))) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), sqr(x1))) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), sqr(x1))) -> c19(A__FIRST(s(z0), a__sqr(mark(x1))))
   MARK(first(x0, add(x1, terms(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(first(x0, add(x1, sqr(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(first(x0, add(x1, add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, add(x1, dbl(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(first(x0, add(x1, first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, add(x1, cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(first(x0, add(x1, recip(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(first(x0, add(x1, s(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(first(x0, add(x1, 0))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(first(x0, add(x1, nil))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(first(x0, add(terms(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, add(sqr(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, add(add(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(first(x0, add(dbl(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, add(first(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(first(x0, add(cons(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(first(x0, add(recip(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, add(s(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(first(x0, add(0, x2))) -> c19(A__FIRST(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(first(x0, add(nil, x2))) -> c19(A__FIRST(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(first(terms(z0), add(x1, x2))) -> c19(A__FIRST(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(first(sqr(z0), add(x1, x2))) -> c19(A__FIRST(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(first(add(z0, z1), add(x1, x2))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(first(dbl(z0), add(x1, x2))) -> c19(A__FIRST(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(first(first(z0, z1), add(x1, x2))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(first(x0, add(x1, x2))) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), add(x1, x2))) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), add(x1, x2))) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), add(x1, x2))) -> c19(A__FIRST(s(z0), a__add(mark(x1), mark(x2))))
   MARK(first(x0, dbl(terms(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0))
   MARK(first(x0, dbl(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0))
   MARK(first(x0, dbl(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, dbl(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0))
   MARK(first(x0, dbl(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, dbl(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0))
   MARK(first(x0, dbl(recip(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0))
   MARK(first(x0, dbl(s(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(s(z0))), MARK(x0))
   MARK(first(x0, dbl(0))) -> c19(A__FIRST(mark(x0), a__dbl(0)), MARK(x0))
   MARK(first(x0, dbl(nil))) -> c19(A__FIRST(mark(x0), a__dbl(nil)), MARK(x0))
   MARK(first(terms(z0), dbl(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0)))
   MARK(first(sqr(z0), dbl(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0)))
   MARK(first(add(z0, z1), dbl(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1)))
   MARK(first(dbl(z0), dbl(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0)))
   MARK(first(first(z0, z1), dbl(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1)))
   MARK(first(x0, dbl(x1))) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), dbl(x1))) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), dbl(x1))) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), dbl(x1))) -> c19(A__FIRST(s(z0), a__dbl(mark(x1))))
   MARK(first(x0, first(x1, x2))) -> c19(A__FIRST(mark(x0), first(mark(x1), mark(x2))), MARK(x0))
   MARK(first(x0, first(x1, terms(z0)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(first(x0, first(x1, sqr(z0)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(first(x0, first(x1, add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, first(x1, dbl(z0)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(first(x0, first(x1, first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, first(x1, cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(first(x0, first(x1, recip(z0)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(first(x0, first(x1, s(z0)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), s(z0))), MARK(x0))
   MARK(first(x0, first(x1, 0))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0))
   MARK(first(x0, first(x1, nil))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0))
   MARK(first(x0, first(terms(z0), x2))) -> c19(A__FIRST(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, first(sqr(z0), x2))) -> c19(A__FIRST(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, first(add(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(first(x0, first(dbl(z0), x2))) -> c19(A__FIRST(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, first(first(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(first(x0, first(cons(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(first(x0, first(recip(z0), x2))) -> c19(A__FIRST(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, first(s(z0), x2))) -> c19(A__FIRST(mark(x0), a__first(s(z0), mark(x2))), MARK(x0))
   MARK(first(x0, first(0, x2))) -> c19(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0))
   MARK(first(x0, first(nil, x2))) -> c19(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0))
   MARK(first(terms(z0), first(x1, x2))) -> c19(A__FIRST(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(first(sqr(z0), first(x1, x2))) -> c19(A__FIRST(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(first(add(z0, z1), first(x1, x2))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(first(dbl(z0), first(x1, x2))) -> c19(A__FIRST(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(first(first(z0, z1), first(x1, x2))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(first(cons(z0, z1), first(x1, x2))) -> c19(A__FIRST(cons(mark(z0), z1), a__first(mark(x1), mark(x2))), MARK(cons(z0, z1)))
   MARK(first(recip(z0), first(x1, x2))) -> c19(A__FIRST(recip(mark(z0)), a__first(mark(x1), mark(x2))), MARK(recip(z0)))
   MARK(first(s(z0), first(x1, x2))) -> c19(A__FIRST(s(z0), a__first(mark(x1), mark(x2))), MARK(s(z0)))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2


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

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

(220)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
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   MARK(add(first(x0, terms(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, sqr(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   MARK(add(first(x0, dbl(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2))
   MARK(add(first(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2))
   MARK(add(first(x0, recip(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2))
   MARK(add(first(x0, s(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(x2))
   MARK(add(first(x0, 0), x2)) -> c17(A__ADD(a__first(mark(x0), 0), mark(x2)), MARK(x2))
   MARK(add(first(x0, nil), x2)) -> c17(A__ADD(a__first(mark(x0), nil), mark(x2)), MARK(x2))
   MARK(add(first(terms(z0), x1), x2)) -> c17(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(sqr(z0), x1), x2)) -> c17(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(add(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(dbl(z0), x1), x2)) -> c17(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(first(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(recip(z0), x1), x2)) -> c17(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(s(z0), x1), x2)) -> c17(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(0, x1), x2)) -> c17(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(nil, x1), x2)) -> c17(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(x2))
   MARK(add(first(x0, x1), s(z0))) -> c17(A__ADD(a__first(mark(x0), mark(x1)), s(z0)))
   MARK(add(first(x0, x1), 0)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), 0))
   MARK(add(first(x0, x1), nil)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), nil))
   MARK(add(first(x0, x1), x2)) -> c17(MARK(x2))
   MARK(add(0, s(x1))) -> c17(A__ADD(0, s(x1)))
   MARK(add(0, 0)) -> c17(A__ADD(0, 0))
   MARK(add(0, nil)) -> c17(A__ADD(0, nil))
   MARK(first(x0, terms(x1))) -> c19(A__FIRST(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(first(x0, terms(terms(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(first(x0, terms(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(first(x0, terms(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, terms(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(first(x0, terms(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, terms(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(first(x0, terms(recip(z0)))) -> c19(A__FIRST(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(first(x0, terms(s(z0)))) -> c19(A__FIRST(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(first(x0, terms(0))) -> c19(A__FIRST(mark(x0), a__terms(0)), MARK(x0))
   MARK(first(x0, terms(nil))) -> c19(A__FIRST(mark(x0), a__terms(nil)), MARK(x0))
   MARK(first(terms(z0), terms(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(first(sqr(z0), terms(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(first(add(z0, z1), terms(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(first(dbl(z0), terms(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(first(first(z0, z1), terms(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(first(x0, terms(x1))) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), terms(x1))) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), terms(x1))) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), terms(x1))) -> c19(A__FIRST(s(z0), a__terms(mark(x1))))
   MARK(first(x0, sqr(terms(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(first(x0, sqr(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(first(x0, sqr(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, sqr(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(first(x0, sqr(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, sqr(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(first(x0, sqr(recip(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(first(x0, sqr(s(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(first(x0, sqr(0))) -> c19(A__FIRST(mark(x0), a__sqr(0)), MARK(x0))
   MARK(first(x0, sqr(nil))) -> c19(A__FIRST(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(first(terms(z0), sqr(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(first(sqr(z0), sqr(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(first(add(z0, z1), sqr(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(first(dbl(z0), sqr(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(first(first(z0, z1), sqr(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(first(x0, sqr(x1))) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), sqr(x1))) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), sqr(x1))) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), sqr(x1))) -> c19(A__FIRST(s(z0), a__sqr(mark(x1))))
   MARK(first(x0, add(x1, terms(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(first(x0, add(x1, sqr(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(first(x0, add(x1, add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, add(x1, dbl(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(first(x0, add(x1, first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, add(x1, cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(first(x0, add(x1, recip(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(first(x0, add(x1, s(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(first(x0, add(x1, 0))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(first(x0, add(x1, nil))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(first(x0, add(terms(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, add(sqr(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, add(add(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(first(x0, add(dbl(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, add(first(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(first(x0, add(cons(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(first(x0, add(recip(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, add(s(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(first(x0, add(0, x2))) -> c19(A__FIRST(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(first(x0, add(nil, x2))) -> c19(A__FIRST(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(first(terms(z0), add(x1, x2))) -> c19(A__FIRST(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(first(sqr(z0), add(x1, x2))) -> c19(A__FIRST(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(first(add(z0, z1), add(x1, x2))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(first(dbl(z0), add(x1, x2))) -> c19(A__FIRST(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(first(first(z0, z1), add(x1, x2))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(first(x0, add(x1, x2))) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), add(x1, x2))) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), add(x1, x2))) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), add(x1, x2))) -> c19(A__FIRST(s(z0), a__add(mark(x1), mark(x2))))
   MARK(first(x0, dbl(terms(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0))
   MARK(first(x0, dbl(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0))
   MARK(first(x0, dbl(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, dbl(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0))
   MARK(first(x0, dbl(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, dbl(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0))
   MARK(first(x0, dbl(recip(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0))
   MARK(first(x0, dbl(s(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(s(z0))), MARK(x0))
   MARK(first(x0, dbl(0))) -> c19(A__FIRST(mark(x0), a__dbl(0)), MARK(x0))
   MARK(first(x0, dbl(nil))) -> c19(A__FIRST(mark(x0), a__dbl(nil)), MARK(x0))
   MARK(first(terms(z0), dbl(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0)))
   MARK(first(sqr(z0), dbl(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0)))
   MARK(first(add(z0, z1), dbl(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1)))
   MARK(first(dbl(z0), dbl(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0)))
   MARK(first(first(z0, z1), dbl(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1)))
   MARK(first(x0, dbl(x1))) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), dbl(x1))) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), dbl(x1))) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), dbl(x1))) -> c19(A__FIRST(s(z0), a__dbl(mark(x1))))
   MARK(first(x0, first(x1, terms(z0)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(first(x0, first(x1, sqr(z0)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(first(x0, first(x1, add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, first(x1, dbl(z0)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(first(x0, first(x1, first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, first(x1, cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(first(x0, first(x1, recip(z0)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(first(x0, first(x1, s(z0)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), s(z0))), MARK(x0))
   MARK(first(x0, first(x1, 0))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0))
   MARK(first(x0, first(x1, nil))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0))
   MARK(first(x0, first(terms(z0), x2))) -> c19(A__FIRST(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, first(sqr(z0), x2))) -> c19(A__FIRST(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, first(add(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(first(x0, first(dbl(z0), x2))) -> c19(A__FIRST(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, first(first(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(first(x0, first(cons(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(first(x0, first(recip(z0), x2))) -> c19(A__FIRST(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, first(s(z0), x2))) -> c19(A__FIRST(mark(x0), a__first(s(z0), mark(x2))), MARK(x0))
   MARK(first(x0, first(0, x2))) -> c19(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0))
   MARK(first(x0, first(nil, x2))) -> c19(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0))
   MARK(first(terms(z0), first(x1, x2))) -> c19(A__FIRST(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(first(sqr(z0), first(x1, x2))) -> c19(A__FIRST(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(first(add(z0, z1), first(x1, x2))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(first(dbl(z0), first(x1, x2))) -> c19(A__FIRST(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(first(first(z0, z1), first(x1, x2))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(first(x0, first(x1, x2))) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), first(x1, x2))) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), first(x1, x2))) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), first(x1, x2))) -> c19(A__FIRST(s(z0), a__first(mark(x1), mark(x2))))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
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   MARK(first(x0, first(x1, s(z0)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), s(z0))), MARK(x0))
   MARK(first(x0, first(x1, 0))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0))
   MARK(first(x0, first(x1, nil))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0))
   MARK(first(x0, first(terms(z0), x2))) -> c19(A__FIRST(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, first(sqr(z0), x2))) -> c19(A__FIRST(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, first(add(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(first(x0, first(dbl(z0), x2))) -> c19(A__FIRST(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, first(first(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(first(x0, first(cons(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(first(x0, first(recip(z0), x2))) -> c19(A__FIRST(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, first(s(z0), x2))) -> c19(A__FIRST(mark(x0), a__first(s(z0), mark(x2))), MARK(x0))
   MARK(first(x0, first(0, x2))) -> c19(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0))
   MARK(first(x0, first(nil, x2))) -> c19(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0))
   MARK(first(terms(z0), first(x1, x2))) -> c19(A__FIRST(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(first(sqr(z0), first(x1, x2))) -> c19(A__FIRST(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(first(add(z0, z1), first(x1, x2))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(first(dbl(z0), first(x1, x2))) -> c19(A__FIRST(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(first(first(z0, z1), first(x1, x2))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(first(x0, first(x1, x2))) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), first(x1, x2))) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), first(x1, x2))) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), first(x1, x2))) -> c19(A__FIRST(s(z0), a__first(mark(x1), mark(x2))))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2


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

(221) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) by 
   MARK(first(x0, cons(terms(z0), x2))) -> c19(A__FIRST(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0))
   MARK(first(x0, cons(sqr(z0), x2))) -> c19(A__FIRST(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0))
   MARK(first(x0, cons(add(z0, z1), x2))) -> c19(A__FIRST(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0))
   MARK(first(x0, cons(dbl(z0), x2))) -> c19(A__FIRST(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0))
   MARK(first(x0, cons(first(z0, z1), x2))) -> c19(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0))
   MARK(first(x0, cons(cons(z0, z1), x2))) -> c19(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0))
   MARK(first(x0, cons(recip(z0), x2))) -> c19(A__FIRST(mark(x0), cons(recip(mark(z0)), x2)), MARK(x0))
   MARK(first(x0, cons(s(z0), x2))) -> c19(A__FIRST(mark(x0), cons(s(z0), x2)), MARK(x0))
   MARK(first(x0, cons(0, x2))) -> c19(A__FIRST(mark(x0), cons(0, x2)), MARK(x0))
   MARK(first(x0, cons(nil, x2))) -> c19(A__FIRST(mark(x0), cons(nil, x2)), MARK(x0))
   MARK(first(terms(z0), cons(x1, x2))) -> c19(A__FIRST(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(terms(z0)))
   MARK(first(sqr(z0), cons(x1, x2))) -> c19(A__FIRST(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), cons(x1, x2))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), cons(x1, x2))) -> c19(A__FIRST(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), cons(x1, x2))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1)))
   MARK(first(cons(z0, z1), cons(x1, x2))) -> c19(A__FIRST(cons(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(z0, z1)))
   MARK(first(recip(z0), cons(x1, x2))) -> c19(A__FIRST(recip(mark(z0)), cons(mark(x1), x2)), MARK(recip(z0)))
   MARK(first(s(z0), cons(x1, x2))) -> c19(A__FIRST(s(z0), cons(mark(x1), x2)), MARK(s(z0)))
   MARK(first(0, cons(x1, x2))) -> c19(A__FIRST(0, cons(mark(x1), x2)), MARK(0))
   MARK(first(nil, cons(x1, x2))) -> c19(A__FIRST(nil, cons(mark(x1), x2)), MARK(nil))

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

(222)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1)))
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   MARK(first(x0, sqr(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(first(x0, sqr(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, sqr(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(first(x0, sqr(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, sqr(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(first(x0, sqr(recip(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(first(x0, sqr(s(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(first(x0, sqr(0))) -> c19(A__FIRST(mark(x0), a__sqr(0)), MARK(x0))
   MARK(first(x0, sqr(nil))) -> c19(A__FIRST(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(first(terms(z0), sqr(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(first(sqr(z0), sqr(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(first(add(z0, z1), sqr(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(first(dbl(z0), sqr(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(first(first(z0, z1), sqr(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(first(x0, sqr(x1))) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), sqr(x1))) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), sqr(x1))) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), sqr(x1))) -> c19(A__FIRST(s(z0), a__sqr(mark(x1))))
   MARK(first(x0, add(x1, terms(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(first(x0, add(x1, sqr(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(first(x0, add(x1, add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, add(x1, dbl(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(first(x0, add(x1, first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, add(x1, cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(first(x0, add(x1, recip(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(first(x0, add(x1, s(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(first(x0, add(x1, 0))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(first(x0, add(x1, nil))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(first(x0, add(terms(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, add(sqr(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, add(add(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(first(x0, add(dbl(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, add(first(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(first(x0, add(cons(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(first(x0, add(recip(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, add(s(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(first(x0, add(0, x2))) -> c19(A__FIRST(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(first(x0, add(nil, x2))) -> c19(A__FIRST(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(first(terms(z0), add(x1, x2))) -> c19(A__FIRST(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(first(sqr(z0), add(x1, x2))) -> c19(A__FIRST(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(first(add(z0, z1), add(x1, x2))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(first(dbl(z0), add(x1, x2))) -> c19(A__FIRST(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(first(first(z0, z1), add(x1, x2))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(first(x0, add(x1, x2))) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), add(x1, x2))) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), add(x1, x2))) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), add(x1, x2))) -> c19(A__FIRST(s(z0), a__add(mark(x1), mark(x2))))
   MARK(first(x0, dbl(terms(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0))
   MARK(first(x0, dbl(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0))
   MARK(first(x0, dbl(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, dbl(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0))
   MARK(first(x0, dbl(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, dbl(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0))
   MARK(first(x0, dbl(recip(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0))
   MARK(first(x0, dbl(s(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(s(z0))), MARK(x0))
   MARK(first(x0, dbl(0))) -> c19(A__FIRST(mark(x0), a__dbl(0)), MARK(x0))
   MARK(first(x0, dbl(nil))) -> c19(A__FIRST(mark(x0), a__dbl(nil)), MARK(x0))
   MARK(first(terms(z0), dbl(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0)))
   MARK(first(sqr(z0), dbl(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0)))
   MARK(first(add(z0, z1), dbl(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1)))
   MARK(first(dbl(z0), dbl(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0)))
   MARK(first(first(z0, z1), dbl(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1)))
   MARK(first(x0, dbl(x1))) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), dbl(x1))) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), dbl(x1))) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), dbl(x1))) -> c19(A__FIRST(s(z0), a__dbl(mark(x1))))
   MARK(first(x0, first(x1, terms(z0)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(first(x0, first(x1, sqr(z0)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(first(x0, first(x1, add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, first(x1, dbl(z0)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(first(x0, first(x1, first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, first(x1, cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(first(x0, first(x1, recip(z0)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(first(x0, first(x1, s(z0)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), s(z0))), MARK(x0))
   MARK(first(x0, first(x1, 0))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0))
   MARK(first(x0, first(x1, nil))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0))
   MARK(first(x0, first(terms(z0), x2))) -> c19(A__FIRST(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, first(sqr(z0), x2))) -> c19(A__FIRST(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, first(add(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(first(x0, first(dbl(z0), x2))) -> c19(A__FIRST(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, first(first(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(first(x0, first(cons(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(first(x0, first(recip(z0), x2))) -> c19(A__FIRST(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, first(s(z0), x2))) -> c19(A__FIRST(mark(x0), a__first(s(z0), mark(x2))), MARK(x0))
   MARK(first(x0, first(0, x2))) -> c19(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0))
   MARK(first(x0, first(nil, x2))) -> c19(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0))
   MARK(first(terms(z0), first(x1, x2))) -> c19(A__FIRST(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(first(sqr(z0), first(x1, x2))) -> c19(A__FIRST(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(first(add(z0, z1), first(x1, x2))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(first(dbl(z0), first(x1, x2))) -> c19(A__FIRST(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(first(first(z0, z1), first(x1, x2))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(first(x0, first(x1, x2))) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), first(x1, x2))) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), first(x1, x2))) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), first(x1, x2))) -> c19(A__FIRST(s(z0), a__first(mark(x1), mark(x2))))
   MARK(first(x0, cons(terms(z0), x2))) -> c19(A__FIRST(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0))
   MARK(first(x0, cons(sqr(z0), x2))) -> c19(A__FIRST(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0))
   MARK(first(x0, cons(add(z0, z1), x2))) -> c19(A__FIRST(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0))
   MARK(first(x0, cons(dbl(z0), x2))) -> c19(A__FIRST(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0))
   MARK(first(x0, cons(first(z0, z1), x2))) -> c19(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0))
   MARK(first(x0, cons(cons(z0, z1), x2))) -> c19(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0))
   MARK(first(x0, cons(recip(z0), x2))) -> c19(A__FIRST(mark(x0), cons(recip(mark(z0)), x2)), MARK(x0))
   MARK(first(x0, cons(s(z0), x2))) -> c19(A__FIRST(mark(x0), cons(s(z0), x2)), MARK(x0))
   MARK(first(x0, cons(0, x2))) -> c19(A__FIRST(mark(x0), cons(0, x2)), MARK(x0))
   MARK(first(x0, cons(nil, x2))) -> c19(A__FIRST(mark(x0), cons(nil, x2)), MARK(x0))
   MARK(first(terms(z0), cons(x1, x2))) -> c19(A__FIRST(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(terms(z0)))
   MARK(first(sqr(z0), cons(x1, x2))) -> c19(A__FIRST(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), cons(x1, x2))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), cons(x1, x2))) -> c19(A__FIRST(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), cons(x1, x2))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1)))
   MARK(first(cons(z0, z1), cons(x1, x2))) -> c19(A__FIRST(cons(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(z0, z1)))
   MARK(first(recip(z0), cons(x1, x2))) -> c19(A__FIRST(recip(mark(z0)), cons(mark(x1), x2)), MARK(recip(z0)))
   MARK(first(s(z0), cons(x1, x2))) -> c19(A__FIRST(s(z0), cons(mark(x1), x2)), MARK(s(z0)))
   MARK(first(0, cons(x1, x2))) -> c19(A__FIRST(0, cons(mark(x1), x2)), MARK(0))
   MARK(first(nil, cons(x1, x2))) -> c19(A__FIRST(nil, cons(mark(x1), x2)), MARK(nil))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
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   MARK(first(x0, cons(add(z0, z1), x2))) -> c19(A__FIRST(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0))
   MARK(first(x0, cons(dbl(z0), x2))) -> c19(A__FIRST(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0))
   MARK(first(x0, cons(first(z0, z1), x2))) -> c19(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0))
   MARK(first(x0, cons(cons(z0, z1), x2))) -> c19(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0))
   MARK(first(x0, cons(recip(z0), x2))) -> c19(A__FIRST(mark(x0), cons(recip(mark(z0)), x2)), MARK(x0))
   MARK(first(x0, cons(s(z0), x2))) -> c19(A__FIRST(mark(x0), cons(s(z0), x2)), MARK(x0))
   MARK(first(x0, cons(0, x2))) -> c19(A__FIRST(mark(x0), cons(0, x2)), MARK(x0))
   MARK(first(x0, cons(nil, x2))) -> c19(A__FIRST(mark(x0), cons(nil, x2)), MARK(x0))
   MARK(first(terms(z0), cons(x1, x2))) -> c19(A__FIRST(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(terms(z0)))
   MARK(first(sqr(z0), cons(x1, x2))) -> c19(A__FIRST(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), cons(x1, x2))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), cons(x1, x2))) -> c19(A__FIRST(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), cons(x1, x2))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1)))
   MARK(first(cons(z0, z1), cons(x1, x2))) -> c19(A__FIRST(cons(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(z0, z1)))
   MARK(first(recip(z0), cons(x1, x2))) -> c19(A__FIRST(recip(mark(z0)), cons(mark(x1), x2)), MARK(recip(z0)))
   MARK(first(s(z0), cons(x1, x2))) -> c19(A__FIRST(s(z0), cons(mark(x1), x2)), MARK(s(z0)))
   MARK(first(0, cons(x1, x2))) -> c19(A__FIRST(0, cons(mark(x1), x2)), MARK(0))
   MARK(first(nil, cons(x1, x2))) -> c19(A__FIRST(nil, cons(mark(x1), x2)), MARK(nil))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2


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

(223) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing nodes:
   MARK(first(nil, cons(x1, x2))) -> c19(A__FIRST(nil, cons(mark(x1), x2)), MARK(nil))
   MARK(first(0, cons(x1, x2))) -> c19(A__FIRST(0, cons(mark(x1), x2)), MARK(0))

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

(224)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2))))
   MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0))
   MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0))
   MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0))
   MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0))
   MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1))))
   MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0))
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   MARK(first(x0, add(x1, cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(first(x0, add(x1, recip(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(first(x0, add(x1, s(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(first(x0, add(x1, 0))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(first(x0, add(x1, nil))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(first(x0, add(terms(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, add(sqr(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, add(add(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(first(x0, add(dbl(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, add(first(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(first(x0, add(cons(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(first(x0, add(recip(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, add(s(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(first(x0, add(0, x2))) -> c19(A__FIRST(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(first(x0, add(nil, x2))) -> c19(A__FIRST(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(first(terms(z0), add(x1, x2))) -> c19(A__FIRST(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(first(sqr(z0), add(x1, x2))) -> c19(A__FIRST(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(first(add(z0, z1), add(x1, x2))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(first(dbl(z0), add(x1, x2))) -> c19(A__FIRST(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(first(first(z0, z1), add(x1, x2))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(first(x0, add(x1, x2))) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), add(x1, x2))) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), add(x1, x2))) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), add(x1, x2))) -> c19(A__FIRST(s(z0), a__add(mark(x1), mark(x2))))
   MARK(first(x0, dbl(terms(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0))
   MARK(first(x0, dbl(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0))
   MARK(first(x0, dbl(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, dbl(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0))
   MARK(first(x0, dbl(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, dbl(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0))
   MARK(first(x0, dbl(recip(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0))
   MARK(first(x0, dbl(s(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(s(z0))), MARK(x0))
   MARK(first(x0, dbl(0))) -> c19(A__FIRST(mark(x0), a__dbl(0)), MARK(x0))
   MARK(first(x0, dbl(nil))) -> c19(A__FIRST(mark(x0), a__dbl(nil)), MARK(x0))
   MARK(first(terms(z0), dbl(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0)))
   MARK(first(sqr(z0), dbl(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0)))
   MARK(first(add(z0, z1), dbl(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1)))
   MARK(first(dbl(z0), dbl(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0)))
   MARK(first(first(z0, z1), dbl(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1)))
   MARK(first(x0, dbl(x1))) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), dbl(x1))) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), dbl(x1))) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), dbl(x1))) -> c19(A__FIRST(s(z0), a__dbl(mark(x1))))
   MARK(first(x0, first(x1, terms(z0)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(first(x0, first(x1, sqr(z0)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(first(x0, first(x1, add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, first(x1, dbl(z0)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(first(x0, first(x1, first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, first(x1, cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(first(x0, first(x1, recip(z0)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(first(x0, first(x1, s(z0)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), s(z0))), MARK(x0))
   MARK(first(x0, first(x1, 0))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0))
   MARK(first(x0, first(x1, nil))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0))
   MARK(first(x0, first(terms(z0), x2))) -> c19(A__FIRST(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, first(sqr(z0), x2))) -> c19(A__FIRST(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, first(add(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(first(x0, first(dbl(z0), x2))) -> c19(A__FIRST(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, first(first(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(first(x0, first(cons(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(first(x0, first(recip(z0), x2))) -> c19(A__FIRST(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, first(s(z0), x2))) -> c19(A__FIRST(mark(x0), a__first(s(z0), mark(x2))), MARK(x0))
   MARK(first(x0, first(0, x2))) -> c19(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0))
   MARK(first(x0, first(nil, x2))) -> c19(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0))
   MARK(first(terms(z0), first(x1, x2))) -> c19(A__FIRST(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(first(sqr(z0), first(x1, x2))) -> c19(A__FIRST(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(first(add(z0, z1), first(x1, x2))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(first(dbl(z0), first(x1, x2))) -> c19(A__FIRST(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(first(first(z0, z1), first(x1, x2))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(first(x0, first(x1, x2))) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), first(x1, x2))) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), first(x1, x2))) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), first(x1, x2))) -> c19(A__FIRST(s(z0), a__first(mark(x1), mark(x2))))
   MARK(first(x0, cons(terms(z0), x2))) -> c19(A__FIRST(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0))
   MARK(first(x0, cons(sqr(z0), x2))) -> c19(A__FIRST(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0))
   MARK(first(x0, cons(add(z0, z1), x2))) -> c19(A__FIRST(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0))
   MARK(first(x0, cons(dbl(z0), x2))) -> c19(A__FIRST(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0))
   MARK(first(x0, cons(first(z0, z1), x2))) -> c19(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0))
   MARK(first(x0, cons(cons(z0, z1), x2))) -> c19(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0))
   MARK(first(x0, cons(recip(z0), x2))) -> c19(A__FIRST(mark(x0), cons(recip(mark(z0)), x2)), MARK(x0))
   MARK(first(x0, cons(s(z0), x2))) -> c19(A__FIRST(mark(x0), cons(s(z0), x2)), MARK(x0))
   MARK(first(x0, cons(0, x2))) -> c19(A__FIRST(mark(x0), cons(0, x2)), MARK(x0))
   MARK(first(x0, cons(nil, x2))) -> c19(A__FIRST(mark(x0), cons(nil, x2)), MARK(x0))
   MARK(first(terms(z0), cons(x1, x2))) -> c19(A__FIRST(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(terms(z0)))
   MARK(first(sqr(z0), cons(x1, x2))) -> c19(A__FIRST(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), cons(x1, x2))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), cons(x1, x2))) -> c19(A__FIRST(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), cons(x1, x2))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1)))
   MARK(first(cons(z0, z1), cons(x1, x2))) -> c19(A__FIRST(cons(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(z0, z1)))
   MARK(first(recip(z0), cons(x1, x2))) -> c19(A__FIRST(recip(mark(z0)), cons(mark(x1), x2)), MARK(recip(z0)))
   MARK(first(s(z0), cons(x1, x2))) -> c19(A__FIRST(s(z0), cons(mark(x1), x2)), MARK(s(z0)))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
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   MARK(first(s(z0), cons(x1, x2))) -> c19(A__FIRST(s(z0), cons(mark(x1), x2)), MARK(s(z0)))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2


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

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

(226)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0)))
   a__terms(z0) -> terms(z0)
   a__sqr(0) -> 0
   a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0)))
   a__sqr(z0) -> sqr(z0)
   a__dbl(0) -> 0
   a__dbl(s(z0)) -> s(s(dbl(z0)))
   a__dbl(z0) -> dbl(z0)
   a__add(0, z0) -> mark(z0)
   a__add(s(z0), z1) -> s(add(z0, z1))
   a__add(z0, z1) -> add(z0, z1)
   a__first(0, z0) -> nil
   a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2))
   a__first(z0, z1) -> first(z0, z1)
   mark(terms(z0)) -> a__terms(mark(z0))
   mark(sqr(z0)) -> a__sqr(mark(z0))
   mark(add(z0, z1)) -> a__add(mark(z0), mark(z1))
   mark(dbl(z0)) -> a__dbl(mark(z0))
   mark(first(z0, z1)) -> a__first(mark(z0), mark(z1))
   mark(cons(z0, z1)) -> cons(mark(z0), z1)
   mark(recip(z0)) -> recip(mark(z0))
   mark(s(z0)) -> s(z0)
   mark(0) -> 0
   mark(nil) -> nil
Tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2))))
   MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0))
   MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0))
   MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0))
   MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0))
   MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1))))
   MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0))
   MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0))
   MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0))
   MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0)))
   MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2))))
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   MARK(first(x0, dbl(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0))
   MARK(first(x0, dbl(recip(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0))
   MARK(first(x0, dbl(s(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(s(z0))), MARK(x0))
   MARK(first(x0, dbl(0))) -> c19(A__FIRST(mark(x0), a__dbl(0)), MARK(x0))
   MARK(first(x0, dbl(nil))) -> c19(A__FIRST(mark(x0), a__dbl(nil)), MARK(x0))
   MARK(first(terms(z0), dbl(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0)))
   MARK(first(sqr(z0), dbl(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0)))
   MARK(first(add(z0, z1), dbl(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1)))
   MARK(first(dbl(z0), dbl(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0)))
   MARK(first(first(z0, z1), dbl(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1)))
   MARK(first(x0, dbl(x1))) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), dbl(x1))) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), dbl(x1))) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), dbl(x1))) -> c19(A__FIRST(s(z0), a__dbl(mark(x1))))
   MARK(first(x0, first(x1, terms(z0)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(first(x0, first(x1, sqr(z0)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(first(x0, first(x1, add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, first(x1, dbl(z0)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(first(x0, first(x1, first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, first(x1, cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(first(x0, first(x1, recip(z0)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(first(x0, first(x1, s(z0)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), s(z0))), MARK(x0))
   MARK(first(x0, first(x1, 0))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0))
   MARK(first(x0, first(x1, nil))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0))
   MARK(first(x0, first(terms(z0), x2))) -> c19(A__FIRST(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, first(sqr(z0), x2))) -> c19(A__FIRST(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, first(add(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(first(x0, first(dbl(z0), x2))) -> c19(A__FIRST(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, first(first(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(first(x0, first(cons(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(first(x0, first(recip(z0), x2))) -> c19(A__FIRST(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, first(s(z0), x2))) -> c19(A__FIRST(mark(x0), a__first(s(z0), mark(x2))), MARK(x0))
   MARK(first(x0, first(0, x2))) -> c19(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0))
   MARK(first(x0, first(nil, x2))) -> c19(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0))
   MARK(first(terms(z0), first(x1, x2))) -> c19(A__FIRST(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(first(sqr(z0), first(x1, x2))) -> c19(A__FIRST(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(first(add(z0, z1), first(x1, x2))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(first(dbl(z0), first(x1, x2))) -> c19(A__FIRST(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(first(first(z0, z1), first(x1, x2))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(first(x0, first(x1, x2))) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), first(x1, x2))) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), first(x1, x2))) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), first(x1, x2))) -> c19(A__FIRST(s(z0), a__first(mark(x1), mark(x2))))
   MARK(first(x0, cons(terms(z0), x2))) -> c19(A__FIRST(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0))
   MARK(first(x0, cons(sqr(z0), x2))) -> c19(A__FIRST(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0))
   MARK(first(x0, cons(add(z0, z1), x2))) -> c19(A__FIRST(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0))
   MARK(first(x0, cons(dbl(z0), x2))) -> c19(A__FIRST(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0))
   MARK(first(x0, cons(first(z0, z1), x2))) -> c19(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0))
   MARK(first(x0, cons(cons(z0, z1), x2))) -> c19(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0))
   MARK(first(x0, cons(recip(z0), x2))) -> c19(A__FIRST(mark(x0), cons(recip(mark(z0)), x2)), MARK(x0))
   MARK(first(x0, cons(s(z0), x2))) -> c19(A__FIRST(mark(x0), cons(s(z0), x2)), MARK(x0))
   MARK(first(x0, cons(0, x2))) -> c19(A__FIRST(mark(x0), cons(0, x2)), MARK(x0))
   MARK(first(x0, cons(nil, x2))) -> c19(A__FIRST(mark(x0), cons(nil, x2)), MARK(x0))
   MARK(first(terms(z0), cons(x1, x2))) -> c19(A__FIRST(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(terms(z0)))
   MARK(first(sqr(z0), cons(x1, x2))) -> c19(A__FIRST(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), cons(x1, x2))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), cons(x1, x2))) -> c19(A__FIRST(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), cons(x1, x2))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1)))
   MARK(first(cons(z0, z1), cons(x1, x2))) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), cons(x1, x2))) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), cons(x1, x2))) -> c19(A__FIRST(s(z0), cons(mark(x1), x2)))
S tuples:
   A__ADD(0, z0) -> c8(MARK(z0))
   A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1))
   MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0))
   MARK(cons(z0, z1)) -> c21(MARK(z0))
   MARK(recip(z0)) -> c22(MARK(z0))
   A__TERMS(z0) -> c(MARK(z0))
   MARK(sqr(z0)) -> c15(MARK(z0))
   MARK(dbl(z0)) -> c18(MARK(z0))
   MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0)))
   MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)))
   MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1))
   MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1))
   MARK(add(recip(z0), x1)) -> c17(MARK(x1))
   MARK(add(s(z0), x1)) -> c17(MARK(x1))
   MARK(add(nil, x1)) -> c17(MARK(x1))
   MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0)))
   MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1)))
   MARK(first(x0, recip(z0))) -> c19(MARK(x0))
   MARK(first(x0, s(z0))) -> c19(MARK(x0))
   MARK(first(x0, 0)) -> c19(MARK(x0))
   MARK(first(x0, nil)) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)))
   MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0)))
   MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0)))
   MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1)))
   MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0)))
   MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1)))
   MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1)))
   MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1))
   MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1))
   MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0)))
   MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1))
   MARK(first(recip(z0), x1)) -> c20(MARK(x1))
   MARK(first(0, x1)) -> c20(MARK(x1))
   MARK(first(nil, x1)) -> c20(MARK(x1))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0))
   MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0))
   MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0))
   MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0))
   MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0))
   MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))))
   MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0))
   MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0))
   MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1)))
   MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0)))
   MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))))
   MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0))
   MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
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   MARK(first(add(z0, z1), terms(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1)))
   MARK(first(dbl(z0), terms(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0)))
   MARK(first(first(z0, z1), terms(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1)))
   MARK(first(x0, terms(x1))) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), terms(x1))) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), terms(x1))) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), terms(x1))) -> c19(A__FIRST(s(z0), a__terms(mark(x1))))
   MARK(first(x0, sqr(terms(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0))
   MARK(first(x0, sqr(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0))
   MARK(first(x0, sqr(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, sqr(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0))
   MARK(first(x0, sqr(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, sqr(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0))
   MARK(first(x0, sqr(recip(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0))
   MARK(first(x0, sqr(s(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(s(z0))), MARK(x0))
   MARK(first(x0, sqr(0))) -> c19(A__FIRST(mark(x0), a__sqr(0)), MARK(x0))
   MARK(first(x0, sqr(nil))) -> c19(A__FIRST(mark(x0), a__sqr(nil)), MARK(x0))
   MARK(first(terms(z0), sqr(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0)))
   MARK(first(sqr(z0), sqr(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0)))
   MARK(first(add(z0, z1), sqr(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1)))
   MARK(first(dbl(z0), sqr(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0)))
   MARK(first(first(z0, z1), sqr(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1)))
   MARK(first(x0, sqr(x1))) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), sqr(x1))) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), sqr(x1))) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), sqr(x1))) -> c19(A__FIRST(s(z0), a__sqr(mark(x1))))
   MARK(first(x0, add(x1, terms(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(first(x0, add(x1, sqr(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(first(x0, add(x1, add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, add(x1, dbl(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(first(x0, add(x1, first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, add(x1, cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(first(x0, add(x1, recip(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(first(x0, add(x1, s(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), s(z0))), MARK(x0))
   MARK(first(x0, add(x1, 0))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), 0)), MARK(x0))
   MARK(first(x0, add(x1, nil))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), nil)), MARK(x0))
   MARK(first(x0, add(terms(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, add(sqr(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, add(add(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(first(x0, add(dbl(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, add(first(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(first(x0, add(cons(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(first(x0, add(recip(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, add(s(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(s(z0), mark(x2))), MARK(x0))
   MARK(first(x0, add(0, x2))) -> c19(A__FIRST(mark(x0), a__add(0, mark(x2))), MARK(x0))
   MARK(first(x0, add(nil, x2))) -> c19(A__FIRST(mark(x0), a__add(nil, mark(x2))), MARK(x0))
   MARK(first(terms(z0), add(x1, x2))) -> c19(A__FIRST(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(first(sqr(z0), add(x1, x2))) -> c19(A__FIRST(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(first(add(z0, z1), add(x1, x2))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(first(dbl(z0), add(x1, x2))) -> c19(A__FIRST(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(first(first(z0, z1), add(x1, x2))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(first(x0, add(x1, x2))) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), add(x1, x2))) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), add(x1, x2))) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), add(x1, x2))) -> c19(A__FIRST(s(z0), a__add(mark(x1), mark(x2))))
   MARK(first(x0, dbl(terms(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0))
   MARK(first(x0, dbl(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0))
   MARK(first(x0, dbl(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, dbl(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0))
   MARK(first(x0, dbl(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, dbl(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0))
   MARK(first(x0, dbl(recip(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0))
   MARK(first(x0, dbl(s(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(s(z0))), MARK(x0))
   MARK(first(x0, dbl(0))) -> c19(A__FIRST(mark(x0), a__dbl(0)), MARK(x0))
   MARK(first(x0, dbl(nil))) -> c19(A__FIRST(mark(x0), a__dbl(nil)), MARK(x0))
   MARK(first(terms(z0), dbl(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0)))
   MARK(first(sqr(z0), dbl(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0)))
   MARK(first(add(z0, z1), dbl(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1)))
   MARK(first(dbl(z0), dbl(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0)))
   MARK(first(first(z0, z1), dbl(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1)))
   MARK(first(x0, dbl(x1))) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), dbl(x1))) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), dbl(x1))) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), dbl(x1))) -> c19(A__FIRST(s(z0), a__dbl(mark(x1))))
   MARK(first(x0, first(x1, terms(z0)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0))
   MARK(first(x0, first(x1, sqr(z0)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0))
   MARK(first(x0, first(x1, add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, first(x1, dbl(z0)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0))
   MARK(first(x0, first(x1, first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0))
   MARK(first(x0, first(x1, cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0))
   MARK(first(x0, first(x1, recip(z0)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0))
   MARK(first(x0, first(x1, s(z0)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), s(z0))), MARK(x0))
   MARK(first(x0, first(x1, 0))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0))
   MARK(first(x0, first(x1, nil))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0))
   MARK(first(x0, first(terms(z0), x2))) -> c19(A__FIRST(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, first(sqr(z0), x2))) -> c19(A__FIRST(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, first(add(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(first(x0, first(dbl(z0), x2))) -> c19(A__FIRST(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, first(first(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0))
   MARK(first(x0, first(cons(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0))
   MARK(first(x0, first(recip(z0), x2))) -> c19(A__FIRST(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0))
   MARK(first(x0, first(s(z0), x2))) -> c19(A__FIRST(mark(x0), a__first(s(z0), mark(x2))), MARK(x0))
   MARK(first(x0, first(0, x2))) -> c19(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0))
   MARK(first(x0, first(nil, x2))) -> c19(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0))
   MARK(first(terms(z0), first(x1, x2))) -> c19(A__FIRST(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0)))
   MARK(first(sqr(z0), first(x1, x2))) -> c19(A__FIRST(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0)))
   MARK(first(add(z0, z1), first(x1, x2))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1)))
   MARK(first(dbl(z0), first(x1, x2))) -> c19(A__FIRST(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0)))
   MARK(first(first(z0, z1), first(x1, x2))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1)))
   MARK(first(x0, first(x1, x2))) -> c19(MARK(x0))
   MARK(first(cons(z0, z1), first(x1, x2))) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), first(x1, x2))) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), first(x1, x2))) -> c19(A__FIRST(s(z0), a__first(mark(x1), mark(x2))))
   MARK(first(x0, cons(terms(z0), x2))) -> c19(A__FIRST(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0))
   MARK(first(x0, cons(sqr(z0), x2))) -> c19(A__FIRST(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0))
   MARK(first(x0, cons(add(z0, z1), x2))) -> c19(A__FIRST(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0))
   MARK(first(x0, cons(dbl(z0), x2))) -> c19(A__FIRST(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0))
   MARK(first(x0, cons(first(z0, z1), x2))) -> c19(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0))
   MARK(first(x0, cons(cons(z0, z1), x2))) -> c19(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0))
   MARK(first(x0, cons(recip(z0), x2))) -> c19(A__FIRST(mark(x0), cons(recip(mark(z0)), x2)), MARK(x0))
   MARK(first(x0, cons(s(z0), x2))) -> c19(A__FIRST(mark(x0), cons(s(z0), x2)), MARK(x0))
   MARK(first(x0, cons(0, x2))) -> c19(A__FIRST(mark(x0), cons(0, x2)), MARK(x0))
   MARK(first(x0, cons(nil, x2))) -> c19(A__FIRST(mark(x0), cons(nil, x2)), MARK(x0))
   MARK(first(terms(z0), cons(x1, x2))) -> c19(A__FIRST(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(terms(z0)))
   MARK(first(sqr(z0), cons(x1, x2))) -> c19(A__FIRST(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(sqr(z0)))
   MARK(first(add(z0, z1), cons(x1, x2))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(add(z0, z1)))
   MARK(first(dbl(z0), cons(x1, x2))) -> c19(A__FIRST(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0)))
   MARK(first(first(z0, z1), cons(x1, x2))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1)))
   MARK(first(cons(z0, z1), cons(x1, x2))) -> c19(MARK(cons(z0, z1)))
   MARK(first(recip(z0), cons(x1, x2))) -> c19(MARK(recip(z0)))
   MARK(first(s(z0), cons(x1, x2))) -> c19(A__FIRST(s(z0), cons(mark(x1), x2)))
K tuples:none
Defined Rule Symbols:   a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1

Defined Pair Symbols:   A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1

Compound Symbols:   c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2